.DonMcD.Pgms.maths.BigNum.sumryf241Q careful. xxx
02.03.03   17:37
==========

(higher filtering of primes. ?? prog c24. c241Q  c22Byte 8-3-2003.)

please increment by 30030 not 60060.
11.03.03  23:19

however found factor 4643671 and 9.79 million.
not 237379x

limits 60037*60041^2 ok. bugs. 2^52+1=17*858001* use prog facthcf.
 3^33+30 etc. ok.= 3*47*549167*71792299.


(higher filtering of primes. ?? prog c24. c241Q  c22Byte 8-3-2003.)

limits 60037*60041^2 ok. bugs. 2^52+1=17*858001* use prog facthcf.
 3^33+30 etc. ok.= 3*47*549167*71792299.

my file > *ram.sumryfact.creditcd1..  Wed,12 Mar 2003.23:15:15
by don.mcdonald.pgm.c22Bc. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

== LETTER values : C,A,T = 03,01,20. (BASE 100, Altern. base 27, keypad)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  45E14..=4500000000000000
= 2^2*3*3*5*5*2^8*5*5*5*5*5*5*5*5*2^4*5*5*5*5*5*all 13cs

3  p(2)+prob..=4500000000000003= 3*3631*413109336271prime 1mn
4  p(2)+prob..=4500000000000004= 2^2*269*438527*9536827prime 45s.
5  p(2)+prob..=4500000000000005= 5*1097*820419325433prime 1mn
6  p(2)+prob..=4500000000000006= 2*3*?1222717*613388053prime 1mn
7  p(2)+prob..=4500000000000007= ? 8mn
8  p(2)+prob..=4500000000000008= 2^2*7*2*47*131*5569*2343571*all 1s.
9  p(2)+prob..=4500000000000009= 3*3*3*? 8mn
10  p(2)+prob..=4500000000000010= 2*5*11*787*51981055793prime 29s.
11  p(2)+prob..=4500000000000011= 13*31*71*337*4793*97367*all 46cs
continu.
12  p(2)+prob..=4500000000000012= 2^2*3*23*16304347826087prime 5mn
13  p(2)+prob..=4500000000000013= 521*8637236084453prime 4mn

15  p(2)+prob..=4500000000000015= 3*5*7*95773*447486691prime 18s.
16  p(2)+prob..=4500000000000016= 2^2*2^2*29*41*351347*673247prime 38s.
17  p(2)+prob..=4500000000000017= 277*16245487364621prime 5mn
18  p(2)+prob..=4500000000000018= 2*3*3*?648931*385248971prime 57s.
19  p(2)+prob..=4500000000000019= 61*1663*44359886833prime 29s.
20  p(2)+prob..=4500000000000020= 2^2*5*?4811909*46758989prime 6mn
contin.


?0
enter = close ,  or <ESC> resume.?
e n d. prog c241Q  24.2.03   close *spool


my file > *ram.sumryfact.creditcd1..  Tue,11 Mar 2003.23:13:25
by don.mcdonald.pgm.c22Bc. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

== LETTER values : C,A,T = 03,01,20. (BASE 100, Altern. base 27, keypad)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  60037*60041^2 ? exam..=216428682962197= 60037*60041*60041*all 10s.
3  2^prob-1..=7= 7*all 2cs
4  2^prob-1..=15= 3*5*all 2cs
5  2^prob-1..=31= 31*all 2cs
6  2^prob-1..=63= 3*3*7*all 2cs
7  2^prob-1..=127= 127*all 2cs
8  2^prob-1..=255= 3*5*17*all 3cs
9  2^prob-1..=511= 7*73*all 3cs
10  2^prob-1..=1023= 3*11*31*all 3cs
11  2^prob-1..=2047= 23*89*all 3cs


12  2^prob-1..=4095= 3*3*5*7*13*all 4cs
13  2^prob-1..=8191= 8191*all 4cs
14  2^prob-1..=16383= 3*43*127*all 4cs
15  2^prob-1..=32767= 7*31*151*all 4cs
16  2^prob-1..=65535= 3*5*17*257*all 4cs
17  2^prob-1..=131071= 131071*all 6cs
18  2^prob-1..=262143= 3*3*3*7*19*73*all 5cs
19  2^prob-1..=524287= 524287*all 9cs
20  2^prob-1..=1048575= 3*5*5*11*31*41*all 5cs
21  2^prob-1..=2097151= 7*7*127*337*all 5cs
22  2^prob-1..=4194303= 3*23*89*683*all 6cs
23  2^prob-1..=8388607= 47*178481*all 8cs
24  2^prob-1..=16777215= 3*3*5*7*13*17*241*all 5cs
25  2^prob-1..=33554431= 31*601*1801*all 9cs
26  2^prob-1..=67108863= 3*2731*8191*all 22cs
27  2^prob-1..=134217727= 7*73*262657*all 8cs
28  2^prob-1..=268435455= 3*5*29*43*113*127*all 6cs
29  2^prob-1..=536870911= 233*1103*2089*all 12cs
30  2^prob-1..=1073741823= 3*3*7*11*31*151*331*all 7cs
31  2^prob-1..=2147483647= 2147483647*all 2s.


32  2^prob-1..=4294967295= 3*5*17*257*65537*all 9cs
33  2^prob-1..=8589934591= 7*23*89*599479*all 12cs
34  2^prob-1..=17179869183= 3*43691*131071*all 6s.
35  2^prob-1..=34359738367= 31*71*127*122921*all 11cs
36  2^prob-1..=68719476735= 3*3*5*7*13*19*3*37*73*109*all 9cs
37  2^prob-1..=137438953471= 223*616318177*all 1s.
38  2^prob-1..=274877906943= 3*174763*524287prime 24s.
39  2^prob-1..=549755813887= 7*79*8191*121369*all 59cs
40  2^prob-1..=1099511627775= 3*5*5*11*17*31*41*61681*all 11cs
41  2^prob-1..=2199023255551= 13367*164511353*all 2s.
42  2^prob-1..=4398046511103= 3*3*7*7*43*127*337*5419*all 13cs
43  2^prob-1..=8796093022207= 431*9719*2099863*all 1s.
44  2^prob-1..=17592186044415= 3*5*23*89*397*683*2113*all 17cs
45  2^prob-1..=35184372088831= 7*31*73*151*631*23311*all 18cs
46  2^prob-1..=70368744177663= 3*47*178481*2796203prime 24s.
47  2^prob-1..=140737488355327= 2351*4513*13264529*all 1s.
48  2^prob-1..=281474976710655= 3*3*5*7*13*17*97*241*257*673*all 14cs
49  2^prob-1..=562949953421311= 127*4432676798593prime 2mn
50  2^prob-1..=1125899906842623= 3*11*31*251*601*1801*4051*all 32cs
51  2^prob-1..=2251799813685247= 7*103*2143*11119*131071*all 1s.


52  2^prob-1..=4503599627370495= 3*5*53*157*1613*2731*8191*all 54cs
53  2^prob-1..=9007199254740991= Accy?(3*2*2*2*2*2*3*2*3*2*3*2*2^2*5*2*3*2*3*603298561*all 1s.
54  2^prob-1..=18014398509481984= Accy?(squ of(3th powof(3th powof(3th powof(2*all 3cs
55  3^33..=5559060566555523= Accy?(3th powof(11th powof(3*all 3cs
56  n1+2..=5559060566555525= Accy?(5*5*4643671*47885051prime 6mn
very good.
57  n1+2..=5559060566555527= Accy?(31*43*4170338009419prime 2mn
58  n1+2..=5559060566555529= Accy?(3*11*139*1211916408667prime 1mn
60  n1+2..=5559060566555531= Accy?(7*25307*31380705319prime 25s.
61  n1+2..=5559060566555533= Accy?(8663*641701554491prime 1mn
62  n1+2..=5559060566555535= Accy?(3*5*13*1213*2729*8611969*all 75cs
63  n1+2..=5559060566555537= Accy?(17*53*157*1669*23546189*all 68cs
64  n1+2..=5559060566555539= Accy?(811*6854575297849prime 3mn
65  n1+2..=5559060566555541= Accy?(3*3*29*29*734451125189prime 1mn
66  n1+2..=5559060566555543= Accy?( 4miin     **?? 237379x
67  "failed"(teleph kpd)..=324533= 11*163*181*all 5cs

68  3^33+545-523..=5559060566555545= Accy?(5*7*23*79*2383*36682117*all 88cs
69  n1+2..=5559060566555547= Accy?(3*227*61547*132631721prime 15s.
70  n1+2..=5559060566555549= Accy?(19*37*37*229*2543*366997*all 32cs
71  n1+2..=5559060566555551= Accy?(11*757*797*837634429*all 1s.


72  n1+2..=5559060566555553= Accy?(3*47*549167*71792299prime 53s.
73  n1+2..=5559060566555555= Accy?(5*9797113*113483647prime 12mn
very good.
74  n1+2..=5559060566555557= Accy?(61*103*109*397*20446423*all 46cs
75  n1+2..=5559060566555559= Accy?(3*3*7*7*6073*2075675863*all 3s.
76  n1+2..=5559060566555561= Accy?(13*41*15187*17923*38317*all 3s.
77  n1+2..=5559060566555563= Accy?(101*233*1831*2803*46027*all 58cs
78  n1+2..=5559060566555565= Accy?(3*5*23753*29581*527447*all 4s.
79  n1+2..=5559060566555567= Accy?(6037*471673*1952267prime 47s.
80  n1+2..=5559060566555569= Accy?(1597*3480939615877prime 2mn
81  n1+2..=5559060566555571= Accy?(3*17*2417*45097719313prime 29s.
contin.



(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24. c241Q  c22Byte 8-3-2003.)

limits 60037*60041^2 ok. bugs. 2^52+1=17*858001* use prog facthcf.
 3^33+30 etc. ok.= 3*47*549167*71792299.

my file > *ram.sumryfact.creditcd1..  Tue,11 Mar 2003.01:04:34
by don.mcdonald.pgm.c22Bc. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

== LETTER values : C,A,T = 03,01,20. (BASE 100, Altern. base 27, keypad)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  60037*60041^2 ? exam..=216428682962197= 60037*60041*60041*all 10s.
3  2^52+1..=4503599627370497= Accy?(17*858001*308761441prime 1mn
very good.
4  RND(606)*2*3*5*7*11*..=2619520561588001=  5mn
5  RND(606)*2*3*5*7*11*..=1981337081994371= 383*5173203869437prime 3mn
9  RND(606)*2*3*5*7*11*..=3858783830101253=  17mn


(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24. c241Q  c22Byte 8-3-2003.)

limits 60037*60041^2 ok. bugs. 2^52+1=17*858001* use prog facthcf.
 3^33+30 etc. ok.= 3*47*549167*71792299.

my file > *ram.sumryfact.creditcd1..  Tue,11 Mar 2003.00:27:33
by don.mcdonald.pgm.c22Bc. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

== LETTER values : C,A,T = 03,01,20. (BASE 100, Altern. base 27, keypad)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  60037*60041^2 ? exam..=216428682962197= 60037*60041*60041*all 10s.
3  1E15+3..=1000000000000003= 1000000000000003?try prog facthcf >60061^3 cofactor?14902357*67103479prime 19mn  very good.

5  2^52+1..=4503599627370497= Accy?(17*264917625139441?try prog facthcf >60061^3 cofactor?858001*308761441prime 1mn
6  RND(606)*2*3*5*7*11*..=1135372934626103= 1135372934626103?try prog facthcf >60061^3 cofactor?1062443*1068643621prime 56s.
7  RND(606)*2*3*5*7*11*..=690128646537569= 690128646537569?try prog facthcf >60061^3 cofactor? 5mn

?0
enter = close ,  or <ESC> resume.?
e n d. prog c241Q  24.2.03   close *spool

(higher filtering of primes. ?? prog c24. c241Q c22Byte 24-2-2003.)
limits 60013*60013*60017 bugs.  3^33+30 etc. = 3*47*549167*71792299.

my file > *ram.sumryfact.creditcd1..  Sun,02 Mar 2003.15:49:45
by don.mcdonald.pgm.c22Bc. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

== LETTER values : C,A,T = 03,01,20. (BASE 100, Altern. base 27, keypad)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  60037*60041^2 ? exam..=216428682962197= 60037*60041*60041*all 10s.
3  R%(K%-prob+2)..=2147463453= 3*11923*60037*all 76cs
4  R%(K%-prob+2)..=2147477446= 2*31*577*60029*all 10cs
5  R%(K%-prob+2)..=2147468277= 3*11927*60017*all 76cs
6  R%(K%-prob+2)..=2147445179= 11*3253*60013*all 25cs
7  R%(K%-prob+2)..=2147424209= 7*5113*59999*all 36cs
8  R%(K%-prob+2)..=2147439762= 2*3*3*3*3*13*17*59981*all 8cs
9  R%(K%-prob+2)..=2147441568= 2^5*3*373*59971*all 9cs
10  R%(K%-prob+2)..=2147479869= 3*11939*59957*all 76cs
11  R%(K%-prob+2)..=2147444820= 2^2*3*3*5*199*59951*all 8cs


12  R%(K%-prob+2)..=2147435857= 7*5119*59929*all 36cs
13  R%(K%-prob+2)..=2147448798= 2*3*3*11*181*59921*all 8cs
14  R%(K%-prob+2)..=2147428046= 2*17929*59887*all 1s.
15  R%(K%-prob+2)..=2147440577= 35863*59879*all 2s.

16  P%(I%)..=31583= 31583*all 5cs

17  P%(I%+16-prob)..=31579= 23*1373*all 4cs
18  P%(I%+16-prob)..=31573= 31573*all 4cs
19  P%(I%+16-prob)..=31571= 131*241*all 4cs
20  P%(I%+16-prob)..=31567= 31567*all 5cs
21  P%(I%+16-prob)..=31561= 37*853*all 4cs
22  P%(I%+16-prob)..=31553= 139*227*all 4cs
23  P%(I%+16-prob)..=31547= 31547*all 5cs
24  P%(I%+16-prob)..=31543= 31543*all 5cs
25  P%(I%+16-prob)..=31541= 31541*all 5cs
26  P%(I%+16-prob)..=31531= 31531*all 5cs
27  P%(I%+16-prob)..=31529= 41*769*all 4cs
28  P%(I%+16-prob)..=31523= 29*1087*all 4cs
29  P%(I%+16-prob)..=31519= 43*733*all 4cs
30  P%(I%+16-prob)..=31517= 31517*all 5cs
31  P%(I%+16-prob)..=31513= 31513*all 5cs


32  P%(I%+16-prob)..=31511= 31511*all 5cs
33  P%(I%+16-prob)..=31501= 17*17*109*all 4cs
34  P%(I%+16-prob)..=31489= 31489*all 5cs
35  P%(I%+16-prob)..=31487= 23*37*37*all 4cs
36  P%(I%+16-prob)..=31483= 19*1657*all 4cs
37  P%(I%+16-prob)..=31481= 31481*all 5cs
38  P%(I%+16-prob)..=31477= 31477*all 5cs
39  P%(I%+16-prob)..=31469= 31469*all 5cs
40  P%(I%+16-prob)..=31463= 73*431*all 4cs
41  P%(I%+16-prob)..=31459= 163*193*all 5cs
42  P%(I%+16-prob)..=31457= 83*379*all 4cs
43  P%(I%+16-prob)..=31453= 71*443*all 4cs
44  P%(I%+16-prob)..=31441= 23*1367*all 4cs

45  R%(K%/2+prob)..=1272634267= 35671*35677*all 2s.
46  R%(K%/2+prob)..=1276632899= 35729*35731*all 2s.
47  R%(K%/2+prob)..=1278062491= 35747*35753*all 2s.
48  R%(K%/2+prob)..=1279135189= 35759*35771*all 2s.
49  R%(K%/2+prob)..=1281568397= 35797*35801*all 2s.
50  R%(K%/2+prob)..=1282069627= 35803*35809*all 2s.
51  R%(K%/2+prob)..=1284075547= 35831*35837*all 2s.


52  R%(K%/2+prob)..=1284863989= 35839*35851*all 2s.
53  R%(K%/2+prob)..=1286369947= 35863*35869*all 2s.
54  R%(K%/2+prob)..=1287948463= 35879*35897*all 2s.
55  R%(K%/2+prob)..=1289168989= 35899*35911*all 2s.
56  R%(K%/2+prob)..=1290821159= 35923*35933*all 2s.


57  R%(.95*K%+prob)..=2147474704= 2^4*2287*58687*all 20cs
58  R%(.95*K%+prob)..=2147459484= 2^2*3*3049*58693*all 24cs
59  R%(.95*K%+prob)..=2147444216= 2^3*17*269*58699*all 8cs
60  R%(.95*K%+prob)..=2147472247= 79*463*58711*all 9cs
61  R%(.95*K%+prob)..=2147470209= 3*3*17*239*58727*all 8cs
62  R%(.95*K%+prob)..=2147454679= 36563*58733*all 2s.
63  R%(.95*K%+prob)..=2147453478= 2*3*3*3*677*58741*all 10cs
64  R%(.95*K%+prob)..=2147450836= 2^2*9137*58757*all 60cs
...

172  R%(.95*K%+prob)..=2147435857= 7*5119*59929*all 37cs
173  R%(.95*K%+prob)..=2147444820= 2^2*3*3*5*199*59951*all 8cs
174  R%(.95*K%+prob)..=2147479869= 3*11939*59957*all 76cs
175  R%(.95*K%+prob)..=2147441568= 2^5*3*373*59971*all 8cs
176  R%(.95*K%+prob)..=2147439762= 2*3*3*3*3*13*17*59981*all 8cs
177  R%(.95*K%+prob)..=2147424209= 7*5113*59999*all 36cs
178  R%(.95*K%+prob)..=2147445179= 11*3253*60013*all 25cs
179  R%(.95*K%+prob)..=2147468277= 3*11927*60017*all 76cs
180  R%(.95*K%+prob)..=2147477446= 2*31*577*60029*all 10cs
181  R%(.95*K%+prob)..=2147463453= 3*11923*60037*all 76cs
182  R%(.95*K%+prob)..=2147426406= 2*3*3*1987*60041*all 18cs
183  R%(.95*K%+prob)..=2147445300= 2^2*3*5*5*7*11*13*7151*all 7cs
184  R%(.95*K%+prob)..=0= 1 (less than 2.) 0cs
185  R%(.95*K%+prob)..=0= 1 (less than 2.) 1mn


186  35677..=35677= 35677*all 5cs
187  n1+2..=35679= 3*7*1699*all 4cs
188  n1+2..=35681= 31*1151*all 5cs
189  n1+2..=35683= 17*2099*all 4cs
190  n1+2..=35685= 3*3*5*13*61*all 4cs
191  n1+2..=35687= 127*281*all 5cs


192  n1+2..=35689= 89*401*all 4cs
193  n1+2..=35691= 3*11897*all 5cs
194  n1+2..=35693= 7*5099*all 4cs
195  n1+2..=35695= 5*11*11*59*all 4cs
196  n1+2..=35697= 3*73*163*all 5cs
197  n1+2..=35699= 29*1231*all 4cs
198  n1+2..=35701= 19*1879*all 4cs
199  n1+2..=35703= 3*3*3967*all 4cs
200  n1+2..=35705= 5*37*193*all 4cs
201  n1+2..=35707= 7*5101*all 4cs
202  n1+2..=35709= 3*11903*all 5cs
203  n1+2..=35711= 13*41*67*all 4cs
204  n1+2..=35713= 71*503*all 4cs
205  n1+2..=35715= 3*5*2381*all 4cs
206  n1+2..=35717= 11*17*191*all 4cs
207  n1+2..=35719= 23*1553*all 4cs
208  n1+2..=35721= squ of(3*3*3*7*all 3cs
209  n1+2..=35723= 139*257*all 5cs
210  n1+2..=35725= 5*5*1429*all 4cs
211  n1+2..=35727= 3*11909*all 5cs


212  n1+2..=35729= 35729*all 5cs
213  n-35677..=52= 2^2*13*all 3cs

215  RND(2^15.5)*RND(2^31..=29519128346555= 5*47*179*179*1123*3491*all 21cs
216  RND(2^15.5)*RND(2^31..=1766869166138= 2*15083*58571543*all 3s.
217  RND(2^15.5)*RND(2^31..=11177816617610= 2*5*79*293*6607*7309*all 54cs
218  RND(2^15.5)*RND(2^31..=28048521999960= 2^2*3*3*5*7*11*2*23*331*132911*all 12cs
219  RND(2^15.5)*RND(2^31..=21711783987560= 2^2*5*2*953*7393*77041*all 70cs
220  RND(2^15.5)*RND(2^31..=12992875519329= 3*3*3*3*2549*62928941*all 100cs
221  RND(2^15.5)*RND(2^31..=2240485091208= 2^2*3*3*7*13*2*3*3*3*3*13*324743*all 13cs
222  RND(2^15.5)*RND(2^31..=6239454798614= 2*23*53*283*9043291*all 33cs
223  RND(2^15.5)*RND(2^31..=33688373543616= 2^2*3*11*2^2*2^2*127*125597909*all 79cs
224  RND(2^15.5)*RND(2^31..=1564684209006= 2*3*19*227*607*99611*all 17cs
225  RND(2^15.5)*RND(2^31..=24399247919565= 3*5*19*709*120749501*all 85cs
226  RND(2^15.5)*RND(2^31..=1726283419548= 2^2*3*43*73*97*173*2731*all 14cs


227  RND(2^16)*RND(2^31-1..=34628077297611= 3*3*7*3*3*23*1579*1681649*all 45cs
228  RND(2^16)*RND(2^31-1..=19847320990080= 2^2*3*5*2^2*2^2*2*389*26573641*all 50cs
229  RND(2^16)*RND(2^31-1..=49280756836822= 2*7*41969*83872717*all 6s.
230  RND(2^16)*RND(2^31-1..=302215358888= 2^2*2*29*79*16489271*all 35cs
231  RND(2^16)*RND(2^31-1..=28940155231264= 2^2*2^2*2*67*109*123836759*all 80cs


232  RND(2^16)*RND(2^31-1..=14892495366696= 2^2*3*2*23*7013*3847021*all 1s.
233  RND(2^16)*RND(2^31-1..=414945800880= 2^2*3*5*13*2^2*163*815923*all 15cs
234  RND(2^16)*RND(2^31-1..=6795856472440= 2^2*5*7*2*29*73*1019*11251*all 18cs
235  RND(2^16)*RND(2^31-1..=5133160067126= 2*7*13*2083*13540171*all 67cs
236  RND(2^16)*RND(2^31-1..=88851254406894= 2*3*3*7*877*1433*561109*all 34cs
237  RND(2^16)*RND(2^31-1..=42058652758016= 2^2*2^2*2^2*2^2*2^2*2^2*41*73*631*5437*all 19cs

238  n1/2^12..=10268225771= 41*73*631*5437*all 13cs

239  RND(606)*2*3*5*7*11*..=1432202460018479= 173*683*46643*259867*all 7s.
240  RND(606)*2*3*5*7*11*..=653024955863507= 5927*32783*3360827*all 5s.
241  RND(606)*2*3*5*7*11*..=1988757820129183= 1988757820129183? Gap 59999 >60061^3 cofactor? 10s.
242  RND(606)*2*3*5*7*11*..=2626941299722937= 101*124367*209133611prime 20s.
243  RND(606)*2*3*5*7*11*..=3406118803878019= 35951*94743367469prime 39s.
244  RND(606)*2*3*5*7*11*..=2152014059095099= 61*373*94581552283prime 39s.
245  RND(606)*2*3*5*7*11*..=957275219390543= 2333*8237*49814183*all 1s.
246  RND(606)*2*3*5*7*11*..=3881046044505701= 28661*109841*1232801prime 19s.
247  RND(606)*2*3*5*7*11*..=3309649208125417= 3309649208125417? Gap 59999 >60061^3 cofactor? 10s.
248  RND(606)*2*3*5*7*11*..=4452442880886037= 37*1433*83975083097prime 34s.
249  RND(606)*2*3*5*7*11*..=2352373988734801= 31*314957*240931403prime 35s.
250  RND(606)*2*3*5*7*11*..=1276366959187543= 1276366959187543? Gap 59999 >60061^3 cofactor? 10s.
251  RND(606)*2*3*5*7*11*..=4066564497875947= 127*881*1597*1949*11677*all 49cs


252  RND(606)*2*3*5*7*11*..=541713883841279= 71*7629773011849prime 3mn
253  RND(606)*2*3*5*7*11*..=4482125833425299= 179*25039809125281prime 6mn
254  RND(606)*2*3*5*7*11*..=4482125833425299= 179*25039809125281prime 8mn

255  2^(prob-253)-1..=3= 3*all 2cs
256  2^(prob-253)-1..=7= 7*all 2cs
257  2^(prob-253)-1..=15= 3*5*all 2cs
258  2^(prob-253)-1..=31= 31*all 3cs
259  2^(prob-253)-1..=63= 3*3*7*all 3cs
260  2^(prob-253)-1..=127= 127*all 3cs
261  2^(prob-253)-1..=255= 3*5*17*all 3cs
262  2^(prob-253)-1..=511= 7*73*all 3cs
263  2^(prob-253)-1..=1023= 3*11*31*all 4cs
264  2^(prob-253)-1..=2047= 23*89*all 4cs
265  2^(prob-253)-1..=4095= 3*3*5*7*13*all 4cs
266  2^(prob-253)-1..=8191= 8191*all 5cs
267  2^(prob-253)-1..=16383= 3*43*127*all 4cs
268  2^(prob-253)-1..=32767= 7*31*151*all 5cs
269  2^(prob-253)-1..=65535= 3*5*17*257*all 5cs
270  2^(prob-253)-1..=131071= 131071*all 7cs
271  2^(prob-253)-1..=262143= 3*3*3*7*19*73*all 5cs


272  2^(prob-253)-1..=524287= 524287*all 9cs
273  2^(prob-253)-1..=1048575= 3*5*5*11*31*41*all 6cs
274  2^(prob-253)-1..=2097151= 7*7*127*337*all 5cs
275  2^(prob-253)-1..=4194303= 3*23*89*683*all 6cs
276  2^(prob-253)-1..=8388607= 47*178481*all 8cs
277  2^(prob-253)-1..=16777215= 3*3*5*7*13*17*241*all 6cs
278  2^(prob-253)-1..=33554431= 31*601*1801*all 9cs
279  2^(prob-253)-1..=67108863= 3*2731*8191*all 22cs
280  2^(prob-253)-1..=134217727= 7*73*262657*all 9cs
281  2^(prob-253)-1..=268435455= 3*5*29*43*113*127*all 7cs
282  2^(prob-253)-1..=536870911= 233*1103*2089*all 13cs
283  2^(prob-253)-1..=1073741823= 3*3*7*11*31*151*331*all 8cs
284  2^(prob-253)-1..=2147483647= 2147483647*all 2s.
285  2^(prob-253)-1..=4294967295= 3*5*17*257*65537*all 10cs
286  2^(prob-253)-1..=8589934591= 7*23*89*599479*all 13cs
287  2^(prob-253)-1..=17179869183= 3*43691*131071*all 6s.
288  2^(prob-253)-1..=34359738367= 31*71*127*122921*all 11cs
289  2^(prob-253)-1..=68719476735= 3*3*5*7*13*19*3*37*73*109*all 10cs
290  2^(prob-253)-1..=137438953471= 223*616318177*all 1s.
291  2^(prob-253)-1..=274877906943= 3*174763*524287prime 24s.


292  2^(prob-253)-1..=549755813887= 7*79*8191*121369*all 60cs
293  2^(prob-253)-1..=1099511627775= 3*5*5*11*17*31*41*61681*all 12cs
294  2^(prob-253)-1..=2199023255551= 13367*164511353*all 3s.
295  2^(prob-253)-1..=4398046511103= 3*3*7*7*43*127*337*5419*all 13cs
296  2^(prob-253)-1..=8796093022207= 431*9719*2099863*all 1s.
297  2^(prob-253)-1..=17592186044415= 3*5*23*89*397*683*2113*all 18cs
298  2^(prob-253)-1..=35184372088831= 7*31*73*151*631*23311*all 19cs
299  2^(prob-253)-1..=70368744177663= 3*47*178481*2796203prime 25s.
300  2^(prob-253)-1..=140737488355327= 2351*4513*13264529*all 1s.
301  2^(prob-253)-1..=281474976710655= 3*3*5*7*13*17*97*241*257*673*all 15cs
302  2^(prob-253)-1..=562949953421311= 127*4432676798593prime 2mn
303  2^(prob-253)-1..=1125899906842623= 3*11*31*251*601*1801*4051*all 33cs
304  2^(prob-253)-1..=2251799813685247= 7*103*2143*11119*131071*all 1s.
305  2^(prob-253)-1..=4503599627370495= 3*5*53*157*1613*2731*8191*all 56cs
306  2^(prob-253)-1..=9007199254740991= Accy?(3*2*2*2*2*2*3*2*3*2*3*2*2^2*5*2*3*2*3*603298561*all 1s.

307  2^(prob-253)-1..=18014398509481984= Accy?(squ of(3th powof(3th powof(3th powof(2*all 4cs
308  2^(prob-253)-1..=36028797018963968= Accy?(5th powof(11th powof(2*all 4cs
309  2^(prob-253)-1..=72057594037927936= Accy?(squ of(squ of(squ of(7th powof(2*all 4cs
310  2^(prob-253)-1..=144115188075855872= Accy?(3th powof(19th powof(2*all 5cs
311  2^(prob-253)-1..=288230376151711744= Accy?(squ of(29th powof(2*all 6cs


312  2^(prob-253)-1..=576460752303423488= Accy?(59th powof(2*all 10cs
313  2^(prob-253)-1..=1.15292150460684698E18= Accy?(squ of(squ of(3th powof(5th powof(2*all 4cs
314  2^(prob-253)-1..=2.30584300921369395E18= Accy?(61th powof(2*all 10cs
315  2^(prob-253)-1..=4.6116860184273879E18= Accy?(31th powof(2^2*all 6cs
316  2^(prob-253)-1..=9.22337203685477581E18= Accy?(3th powof(3th powof(7th powof(2*all 4cs
317  2^(prob-253)-1..=1.84467440737095516E19= Accy?(4th powof(4th powof(4th powof(2*all 3cs
318  2^(prob-253)-1..=3.68934881474191032E19= Accy?(5th powof(13th powof(2*all 4cs
319  2^(prob-253)-1..=7.37869762948382065E19= Accy?(3th powof(11th powof(2^2*all 4cs
320  2^(prob-253)-1..=1.47573952589676413E20= Accy?(67th powof(2*all 11cs
321  2^(prob-253)-1..=2.95147905179352826E20= Accy?(4th powof(17th powof(2*all 5cs
322  2^(prob-253)-1..=5.90295810358705652E20= Accy?(3th powof(23th powof(2*all 5cs
323  2^(prob-253)-1..=1.1805916207174113E21= Accy?(5th powof(7th powof(2^2*all 4cs
324  2^(prob-253)-1..=2.36118324143482261E21= Accy?(71th powof(2*all 12cs
325  2^(prob-253)-1..=4.72236648286964521E21= Accy?(3th powof(3th powof(4th powof(2^2*all 3cs
326  2^(prob-253)-1..=9.44473296573929043E21= Accy?(73th powof(2*all 12cs
327  2^(prob-253)-1..=1.88894659314785809E22= Accy?(37th powof(2^2*all 7cs
328  2^(prob-253)-1..=3.77789318629571617E22= Accy?(3th powof(5th powof(5th powof(2*all 3cs
329  2^(prob-253)-1..=7.55578637259143234E22= Accy?(4th powof(19th powof(2*all 5cs
330  2^(prob-253)-1..=1.51115727451828647E23= Accy?(7th powof(11th powof(2*all 4cs
331  2^(prob-253)-1..=3.02231454903657294E23= Accy?(3th powof(13th powof(2^2*all 4cs


332  2^(prob-253)-1..=6.04462909807314587E23= Accy?(79th powof(2*all 13cs
333  2^(prob-253)-1..=1.20892581961462918E24= Accy?(4th powof(4th powof(5th powof(2*all 3cs
334  2^(prob-253)-1..=2.41785163922925835E24= Accy?(3th powof(3th powof(3th powof(3th powof(2*all 3cs
335  2^(prob-253)-1..=4.8357032784585167E24= Accy?(41th powof(2^2*all 8cs
336  2^(prob-253)-1..=9.6714065569170334E24= Accy?(83th powof(2*all 14cs
337  2^(prob-253)-1..=1.93428131138340668E25= Accy?(3th powof(4th powof(7th powof(2*all 4cs
338  2^(prob-253)-1..=3.86856262276681336E25= Accy?(5th powof(17th powof(2*all 5cs
339  2^(prob-253)-1..=7.73712524553362672E25= Accy?(43th powof(2^2*all 8cs
340  2^(prob-253)-1..=1.54742504910672534E26= Accy?(3th powof(29th powof(2*all 6cs
341  2^(prob-253)-1..=3.09485009821345069E26= Accy?(4th powof(11th powof(2^2*all 4cs
342  2^(prob-253)-1..=6.18970019642690138E26= Accy?(89th powof(2*all 14cs
343  2^(prob-253)-1..=1.23794003928538028E27= Accy?(3th powof(3th powof(5th powof(2^2*all 4cs
344  2^(prob-253)-1..=2.47588007857076055E27= Accy?(7th powof(13th powof(2*all 4cs
345  2^(prob-253)-1..=4.9517601571415211E27= Accy?(4th powof(23th powof(2*all 5cs
346  2^(prob-253)-1..=9.9035203142830422E27= Accy?(31th powof(2^3*all 6cs
347  2^(prob-253)-1..=1.98070406285660844E28= Accy?(47th powof(2^2*all 8cs
348  2^(prob-253)-1..=3.96140812571321688E28= Accy?(5th powof(19th powof(2*all 5cs
349  2^(prob-253)-1..=7.92281625142643376E28= Accy?(4th powof(4th powof(6th powof(2*all 4cs
350  2^(prob-253)-1..=1.58456325028528675E29= Accy?(97th powof(2*all 15cs
351  2^(prob-253)-1..=3.1691265005705735E29= Accy?(7th powof(7th powof(2^2*all 3cs


352  2^(prob-253)-1..=6.33825300114114701E29= Accy?(9th powof(11th powof(2*all 4cs
353  2^(prob-253)-1..=1.2676506002282294E30= Accy?(4th powof(5th powof(5th powof(2*all 3cs
354  2^(prob-253)-1..=2.5353012004564588E30= Accy?(101th powof(2*all 16cs
355  2^(prob-253)-1..=5.07060240091291761E30= Accy?(6th powof(17th powof(2*all 5cs
356  2^(prob-253)-1..=1.01412048018258352E31= Accy?(103th powof(2*all 16cs
357  2^(prob-253)-1..=2.02824096036516704E31= Accy?(4th powof(13th powof(2^2*all 4cs
358  2^(prob-253)-1..=4.05648192073033409E31= Accy?(5th powof(7th powof(2^3*all 4cs
359  2^(prob-253)-1..=8.11296384146066817E31= Accy?(53th powof(2^2*all 9cs
360  2^(prob-253)-1..=1.62259276829213363E32= Accy?(107th powof(2*all 17cs
361  2^(prob-253)-1..=3.24518553658426727E32= Accy?(4th powof(9th powof(2^3*all 4cs
362  2^(prob-253)-1..=6.49037107316853454E32= Accy?(109th powof(2*all 17cs
363  2^(prob-253)-1..=1.29807421463370691E33= Accy?(5th powof(11th powof(2^2*all 4cs
364  2^(prob-253)-1..=2.59614842926741381E33= Accy?(37th powof(2^3*all 7cs
365  2^(prob-253)-1..=5.19229685853482763E33= Accy?(4th powof(4th powof(7th powof(2*all 4cs
366  2^(prob-253)-1..=1.03845937170696553E34= Accy?(113th powof(2*all 18cs
contin.

?0
enter = close ,  or <ESC> resume.?
e n d. prog c241Q  24.2.03   close *spool



****        GP/PARI CALCULATOR Version 1.36
                 (Archimedes version)
? isprime(1988757820129183)
this was only large factor that pari resolved by c241q did not.  don.

%1 = 0
? factor(1988757820129183) 
%2 = 
|160967 1 |

|12355065449 1 |


? isprime(3309649208125417)
%3 = 1

? isprime(1276366959187543)
%4 = 1

? isprime(7629773011849)
%5 = 1

? isprime(25039809125281)
%6 = 1

? isprime(4432676798593)
%7 = 1
? #
    timer on
? factor(60037*60041^2)
time = 280 ms
%8 = 
|60037 1 |

|60041 2 |


? nextprime(60041)
time = 10 ms
%9 = 60041

? nextprime(%+1)
time = 30 ms
%10 = 60077
? 2^26-200+1+2
time = 0 ms

%11 = 67108667
? factor(%)
time = 640 ms
%12 = 
|67108667 1 |


? factor(%11+2) 
time = 640 ms
%13 = 
|67108669 1 |      **twin prime under 2^26.


? 3^33
time = 0 ms
%14 = 5559060566555523

? for(n=1,21,x=%14+n;print(factor(x))  )
[2, 2; 7, 1; 67, 1; 661, 1; 25411, 1; 176419, 1]
[5, 2; 4643671, 1; 47885051, 1]
[2, 1; 3, 1; 926510094425921, 1]
[31, 1; 43, 1; 4170338009419, 1]
[2, 3; 1531, 1; 453874964611, 1]
[3, 1; 11, 1; 139, 1; 1211916408667, 1]
[2, 1; 5, 1; 19, 1; 17489, 1; 1672949483, 1]
[7, 1; 25307, 1; 31380705319, 1]
[2, 2; 3, 2; 6883, 1; 22434744889, 1]
[8663, 1; 641701554491, 1]
[2, 1; 2779530283277767, 1]
[3, 1; 5, 1; 13, 1; 1213, 1; 2729, 1; 8611969, 1]
[2, 4; 14051, 1; 24727157171, 1]
[17, 1; 53, 1; 157, 1; 1669, 1; 23546189, 1]
[2, 1; 3, 1; 7, 1; 132358584917989, 1]
[811, 1; 6854575297849, 1]
[2, 2; 5, 1; 11, 1; 223, 1; 85469, 1; 1325761, 1]
[3, 2; 29, 2; 734451125189, 1]
[2, 1; 19051, 1; 145899442721, 1]
[237379, 1; 23418501917, 1]
[2, 3; 3, 1; 163, 1; 1421027752187, 1]
time = 29,970 ms

? for(n=1000,1010,print(factor(Prime(n)*prime(n+1)*prime(n+2))) )
[7919, 1; 7927, 1; 7933, 1]
[7927, 1; 7933, 1; 7937, 1]
[7933, 1; 7937, 1; 7949, 1]
[7937, 1; 7949, 1; 7951, 1]
[7949, 1; 7951, 1; 7963, 1]
[7951, 1; 7963, 1; 7993, 1]
[7963, 1; 7993, 1; 8009, 1]
[7993, 1; 8009, 1; 8011, 1]
[8009, 1; 8011, 1; 8017, 1]
[8011, 1; 8017, 1; 8039, 1]
[8017, 1; 8039, 1; 8053, 1]
time = 480 ms

? for(n=6000,6020,print(factor(Prime(n)*prime(n+1)*prime(n+2))) )
[59359, 1; 59369, 1; 59377, 1]
[59369, 1; 59377, 1; 59387, 1]
[59377, 1; 59387, 1; 59393, 1]
[59387, 1; 59393, 1; 59399, 1]
...

[59513, 1; 59539, 1; 59557, 1]
[59539, 1; 59557, 1; 59561, 1]
[59557, 1; 59561, 1; 59567, 1]
time = 6,180 ms

? ?random
random()=random integer between 0 and 2^31-1.
? factor(random())
time = 630 ms
%15 = 
|5 1 |

|269 1 |

|1580987 1 |


? factor(random()) 
time = 630 ms
%16 = 
|2 4 |

|23 1 |

|414313 1 |


? factor(random())   
time = 10 ms
%17 = 
|2 2 |

|181 1 |

|719 1 |

|3391 1 |


? \q.
*sp.

Yes.  spcopr output from prog 'c21'..c24. c22Bc
end (later)   enter:  0,q,Q, closes *ram.spcopr


prog acorncpusr.c23, c21 c24// c22A. copr2p15.
maths.bignum.c22BC / c241Q test 23.2.03** Sun,02 Mar 2003.17:49:47
IMPORTANT needs *BASIC64.**  (SciCalc) for large nos.
  1.03.01  30.1.02 nzdt*. P%(9+RND(47))
30.5.02 checks that integers are represented with sufficient precision.
24.8.02 square of square and n,nnn, last factor,
24.9.02 11.10.02 Letter values 8x CAP letter word. base 100 and 27.
1.2.03 tel keypad.?? gr harper bday. results p(1),2,3..
prog  c24. 9.2.03, limits 46337*46349*46351 BUG o.k. J% largest 3 factors> 
Progress ... sqrn. 2^62 bugs.
separated h.elp, sumry ERROR 17.
3.11.02  3-53th power..of(,  14.11.02 error sqrt 1 or n<2 fixed? .
10.2.03 consider indirection bit array , rotate shift <<,
 prob^(prob-1)^(prob+1) = 2^1020.
UN. r > 1022, K% =1??, UN. P% >= 2^16, = 2<<16, coprime 2.3.5.7.11.13=30,030.
5760, mod 2.  OR.
10.2.03 squ of( prog c22B


by don.mcdonald@paradise.net.nz  pca.org.nz, 
factorise numbers (Integers)  up to 2^52+1. = 4.5*10^15.

In a hurry?  Do you wish to skip instructions, commentary insights?
enter <RETURN>  yes skip,
  0  no.?
 SET DIR *adfs      dir acorncpusr.donwn*.pi.

PROCoprime2x3x5x7 // x11x13
REM p short coprimes, q +2310K%, R% use, s complement
WONDER IF THIS COULD BE INCR TO 2310/
 2*5760+6 COPRIMES not exceeding prim 2*13#  ?

I13% = 2 passes (13 or 245.)  13  contin
prime I% square  X% 2  4
prime I% square  X% 3  9
prime I% square  X% 5  25
prime I% square  X% 7  49
prime I% square  X% 11  121
prime I% square  X% 13  169
FIRST pass. List coprimes.
highest coprime in sieve = P% (I%) = 11526  60059

Please consider primebase sieve and coprime sieve. 1.3.03

I13% = 2 passes (13 or 245.)  245  contin
prime I% square  X% 2  4
prime I% square  X% 3  9
prime I% square  X% 5  25
prime I% square  X% 7  49
prime I% square  X% 11  121
prime I% square  X% 13  169
prime I% square  X% 17  289
prime I% square  X% 19  361
prime I% square  X% 23  529
prime I% square  X% 29  841
prime I% square  X% 31  961
prime I% square  X% 37  1369
prime I% square  X% 41  1681
prime I% square  X% 43  1849
prime I% square  X% 47  2209
prime I% square  X% 53  2809
prime I% square  X% 59  3481
prime I% square  X% 61  3721
prime I% square  X% 67  4489
prime I% square  X% 71  5041
prime I% square  X% 73  5329
prime I% square  X% 79  6241
prime I% square  X% 83  6889
prime I% square  X% 89  7921
prime I% square  X% 97  9409
prime I% square  X% 101  10201
prime I% square  X% 103  10609
prime I% square  X% 107  11449
prime I% square  X% 109  11881
prime I% square  X% 113  12769
prime I% square  X% 127  16129
prime I% square  X% 131  17161
prime I% square  X% 137  18769
prime I% square  X% 139  19321
prime I% square  X% 149  22201
prime I% square  X% 151  22801
prime I% square  X% 157  24649
prime I% square  X% 163  26569
prime I% square  X% 167  27889
prime I% square  X% 173  29929
prime I% square  X% 179  32041
prime I% square  X% 181  32761
prime I% square  X% 191  36481
prime I% square  X% 193  37249
prime I% square  X% 197  38809
prime I% square  X% 199  39601
prime I% square  X% 211  44521
prime I% square  X% 223  49729
prime I% square  X% 227  51529
prime I% square  X% 229  52441
prime I% square  X% 233  54289
prime I% square  X% 239  57121
prime I% square  X% 241  58081
prime I% square  X% 251  63001
second pass. List actual primes.Q%()
complete 2nd pass.


PROCgenfactbase, generate factor base, R%()

4.2.03 try stronger prime filtering.***********  c24//241Q BUGS. 

copy Q%() = P%() ..+ 2*30030,
  K%=0. R%(K%) =  19# primorial x (2.3.5.7).

Continue ENTER STOP  c$
1= 1 2= 2 3= 3 4= 5 5= 7 6= 11 7= 13 8= 17 9= 19 2.0369349E9= 1
10= 23 11= 29 12= 31 13= 37 14= 41 15= 43 16= 47 2.00783583E9= 2
17= 53 18= 59 19= 61 20= 67 21= 71 22= 73 23= 79 1.80198691E9= 4
24= 83 25= 89 26= 97 27= 101 28= 103 29= 107 2.14105065E9= 5
30= 109 31= 113 32= 127 33= 131 34= 137 35= 139 2.00850856E9= 7
36= 149 37= 151 38= 157 39= 163 40= 167 41= 173 1.85850159E9= 8
42= 179 43= 181 44= 191 45= 193 46= 197 47= 199 2.14112031E9= 10
48= 211 49= 223 50= 227 51= 229 52= 233 53= 239 2.14455867E9= 12
54= 241 55= 251 56= 257 57= 263 58= 269 59= 271 2.13763297E9= 14
60= 277 61= 281 62= 283 63= 293 64= 307 65= 311 2.14362199E9= 16
66= 313 67= 317 68= 331 69= 337 70= 347 71= 349 2.12162394E9= 18
72= 353 73= 359 74= 367 75= 373 76= 379 77= 383 2.11318637E9= 20
78= 389 79= 397 80= 401 81= 409 82= 419 83= 421 2.08357034E9= 22
84= 431 85= 433 86= 439 87= 443 88= 449 89= 457 2.10521353E9= 24
90= 461 91= 463 92= 467 93= 479 94= 487 95= 491 2.07139718E9= 26
96= 499 97= 503 98= 509 99= 521 100= 523 101= 541 2.13424107E9= 28
102= 547 103= 557 104= 563 105= 569 106= 571 2.01200767E9= 29
107= 577 108= 587 109= 593 110= 599 111= 601 2.12736842E9= 31
...
792= 6067 793= 6073 794= 6079 795= 6089 796= 6091 2.14123049E9= 357
797= 6101 798= 6113 799= 6121 800= 6131 801= 6133 2.12583854E9= 359
802= 6143 803= 6151 804= 6163 805= 6173 806= 6197 2.12288233E9= 362
807= 6199 808= 6203 809= 6211 810= 6217 811= 6221 2.11488184E9= 364
812= 6229 813= 6247 814= 6257 815= 6263 816= 6269 2.11072387E9= 367
817= 6271 818= 6277 819= 6287 820= 6299 821= 6301 2.12560562E9= 369
822= 6311 823= 6317 824= 6323 825= 6329 826= 6337 2.11694672E9= 372
827= 6343 828= 6353 829= 6359 830= 6361 831= 6367 2.13574519E9= 374
832= 6373 833= 6379 834= 6389 835= 6397 836= 6421 2.11928241E9= 377
837= 6427 838= 6449 839= 6451 840= 6469 841= 6473 2.11383387E9= 379
842= 6481 843= 6491 844= 6521 845= 6529 846= 6547 2.11639055E9= 382
847= 6551 848= 6553 849= 6563 850= 6569 851= 6571 2.14643515E9= 384
852= 6577 853= 6581 854= 6599 855= 6607 856= 6619 2.12797293E9= 387
857= 6637 858= 6653 859= 6659 860= 6661 861= 6673 2.11948613E9= 389
862= 6679 863= 6689 864= 6691 865= 6701 866= 6703 2.10353665E9= 392
867= 6709 868= 6719 869= 6733 870= 6737 871= 6761 2.11865524E9= 394
872= 6763 873= 6779 874= 6781 875= 6791 876= 6793 2.11454635E9= 397
877= 6803 878= 6823 879= 6827 880= 6829 881= 6833 2.13517597E9= 399
...
5928= 58567 5929= 58573 5930= 58579 5931= 58601 2.1474619E9= 3493
5932= 58603 5933= 58613 5934= 58631 5935= 58657 2.14746309E9= 3497
5936= 58661 5937= 58679 5938= 58687 5939= 58693 2.14747536E9= 3501
5940= 58699 5941= 58711 5942= 58727 5943= 58733 2.14747225E9= 3505
5944= 58741 5945= 58757 5946= 58763 5947= 58771 2.14745084E9= 3509
5948= 58787 5949= 58789 5950= 58831 5951= 58889 2.14744459E9= 3513
5952= 58897 5953= 58901 5954= 58907 5955= 58909 2.14747156E9= 3517
5956= 58913 5957= 58921 5958= 58937 5959= 58943 2.14743477E9= 3521
5960= 58963 5961= 58967 5962= 58979 5963= 58991 2.14746021E9= 3525
5964= 58997 5965= 59009 5966= 59011 5967= 59021 2.14745553E9= 3529
5968= 59023 5969= 59029 5970= 59051 5971= 59053 2.14747502E9= 3533
5972= 59063 5973= 59069 5974= 59077 5975= 59083 2.14745349E9= 3537
5976= 59093 5977= 59107 5978= 59113 5979= 59119 2.14747552E9= 3541
5980= 59123 5981= 59141 5982= 59149 5983= 59159 2.14746885E9= 3545
5984= 59167 5985= 59183 5986= 59197 5987= 59207 2.14745516E9= 3549
5988= 59209 5989= 59219 5990= 59221 5991= 59233 2.1474586E9= 3553
5992= 59239 5993= 59243 5994= 59263 5995= 59273 2.14744026E9= 3557
5996= 59281 5997= 59333 5998= 59341 5999= 59351 2.14743927E9= 3561
6000= 59357 6001= 59359 6002= 59369 6003= 59377 2.14743054E9= 3565
6004= 59387 6005= 59393 6006= 59399 6007= 59407 2.1474727E9= 3569
6008= 59417 6009= 59419 6010= 59441 6011= 59443 2.14746208E9= 3573
6012= 59447 6013= 59453 6014= 59467 6015= 59471 2.14744236E9= 3577
6016= 59473 6017= 59497 6018= 59509 6019= 59513 2.14742522E9= 3581
6020= 59539 6021= 59557 6022= 59561 6023= 59567 2.14744675E9= 3585
6024= 59581 6025= 59611 6026= 59617 6027= 59621 2.14742666E9= 3589
6028= 59627 6029= 59629 6030= 59651 6031= 59659 2.14747881E9= 3593
6032= 59663 6033= 59669 6034= 59671 6035= 59693 2.14742764E9= 3597
6036= 59699 6037= 59707 6038= 59723 6039= 59729 2.14748167E9= 3601
6040= 59743 6041= 59747 6042= 59753 6043= 59771 2.14742667E9= 3605
6044= 59779 6045= 59791 6046= 59797 6047= 59809 2.14745356E9= 3609
6048= 59833 6049= 59863 6050= 59879 6051= 59887 2.1474654E9= 3613
6052= 59921 6053= 59929 6054= 59951 6055= 59957 2.14743586E9= 3617
6056= 59971 6057= 59981 6058= 59999 6059= 60013 2.14743976E9= 3621
6060= 60017 6061= 60029 6062= 60037 6063= 60041 2.14747745E9= 3625
6064= 60060 
query later yes MAT or INDIRECTION
 P%>2*13#  R%(K%)??60060  3628  2.1474453E9
Not XXX YES to worry about primes/ so long as co-prime.

3628  Primorials order 2.1474453E9
Now ready to FIND FACTORS.


A2  B2  C2  D3  E3  F3  G4  H4  I4  
J5  K5  L5  M6  N6  O6  P7  Q7  R7  
S7  T8  U8  V8  W9  X9  Y9  Z9  
telephone keypad.

starting at problem # 1

  Archim. A5000   5-08-01.  18.12.02  4MB RAM,  33 MHz.)
problem # =1.   60037*60041^2 ? example.  = 216428682962197  Repeat n1.

0nothing 0nothing 
  Time speed,  sec = 37.3500000000000014
>>1  0nothing 0nothing  37s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?2^52
2^52 = 4.504E15   ****
2^52 = 4503599627370496 ****
loss of Accuracy*** RESULTS will be WRONG. Contin.
loss of Accuracy*** RESULTS will be WRONG. Contin.
67108864 ^ 2  =  4503599627370496
8192 ^ 2  =  67108864
2 ^ 13  =  8192
PROCf(X%)  
Unknown or missing variable at erl. 4140
problem # =2.   2^52 = 4503599627370496  Repeat n1.

2^52..=4503599627370496= Accy?(squ of(squ of(13th powof(2*all
  Time speed,  sec = 0.04

>>2  2^52..=4503599627370496= Accy?(squ of(squ of(13th powof(2*all 5cs

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?45E15
45E15 = 4.500E16   ****
45E15 = 45000000000000000 ****
loss of Accuracy*** RESULTS will be WRONG. Contin.
loss of Accuracy*** RESULTS will be WRONG. Contin.
45000000000000000=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 55.3207745196401106
PROCf(X%)  REM last factor         17
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 25724787         
progress  45E15..=45000000000000000= Accy?(2^2*17*  +(661764705882353) ? more..

cofactor too big.  Programming fix would need hcf for initial divides.
  n, n/Q%(1) > t = 661764705882353  11018209917.9559612problem # =3.   45E15 = 45000000000000000  Repeat n1.

45E15..=45000000000000000= Accy?(2^2*17*661764705882353? Gap 59999 >60061^3 cofactor?
  Time speed,  sec = 10.7599999999999998
>>3  45E15..=45000000000000000= Accy?(2^2*17*661764705882353? Gap 59999 >60061^3 cofactor? 10s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?45E14
45E14 = 4.500E15   ****
45E14 = 4500000000000000 ****
4500000000000000=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  PROCf(X%)  PROCf(X%)   complete.

Unknown or missing variable at erl. 5440
problem # =4.   45E14 = 4500000000000000  Repeat n1.

45E14..=4500000000000000= 2^2*3*3*5*5*2^8*5*5*5*5*5*5*5*5*2^4*5*5*5*5*5*all
  Time speed,  sec = 0.13

>>4  45E14..=4500000000000000= 2^2*3*3*5*5*2^8*5*5*5*5*5*5*5*5*2^4*5*5*5*5*5*all 13cs

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?p(4)+prob
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000005 ****
4500000000000005=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  REM last factor          5
PROCf(X%)  REM last factor       1097
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 905770 
progress  p(4)+prob..=4500000000000005= 5*1097*  +(820419325433) ? more..
,,,,,,,,,,,,,,,
820419325433 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =5.   p(4)+prob = 4500000000000005  Repeat n1.

p(4)+prob..=4500000000000005= 5*1097*820419325433prime
  Time speed,  sec = 85.9399999999999977
>>5  p(4)+prob..=4500000000000005= 5*1097*820419325433prime 1mn

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000006 ****
4500000000000006=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 27386127         
progress  p(4)+prob..=4500000000000006= 2*3*  +(750000000000001) ? more..

cofactor too big.  Programming fix would need hcf for initial divides.
  n, n/Q%(1) > t = 750000000000001  12487304573.6834393problem # =6.   p(4)+prob = 4500000000000006  Repeat n1.

p(4)+prob..=4500000000000006= 2*3*750000000000001? Gap 59999 >60061^3 cofactor?
  Time speed,  sec = 10.7300000000000004
>>6  p(4)+prob..=4500000000000006= 2*3*750000000000001? Gap 59999 >60061^3 cofactor? 10s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000007 ****
4500000000000007=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 67082039         
progress  p(4)+prob..=4500000000000007=   +(4500000000000007) ? more..

cofactor too big.  Programming fix would need hcf for initial divides.
  n, n/Q%(1) > t = 4500000000000007  74923827442.100647problem # =7.   p(4)+prob = 4500000000000007  Repeat n1.

p(4)+prob..=4500000000000007= 4500000000000007? Gap 59999 >60061^3 cofactor?
  Time speed,  sec = 10.75
>>7  p(4)+prob..=4500000000000007= 4500000000000007? Gap 59999 >60061^3 cofactor? 10s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000008 ****
4500000000000008=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  REM last factor          7
PROCf(X%)  PROCf(X%)  REM last factor         47
PROCf(X%)  REM last factor        131
,,,PROCf(X%)  REM last factor       5569
PROCf(X%)  REM last factor    2343571
 complete.

Unknown or missing variable at erl. 5440
problem # =8.   p(4)+prob = 4500000000000008  Repeat n1.

p(4)+prob..=4500000000000008= 2^2*7*2*47*131*5569*2343571*all
  Time speed,  sec = 1.16999999999999993
>>8  p(4)+prob..=4500000000000008= 2^2*7*2*47*131*5569*2343571*all 1s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000009 ****
4500000000000009=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  PROCf(X%)  ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 12909944         
progress  p(4)+prob..=4500000000000009= 3*3*3*  +(166666666666667) ? more..

cofactor too big.  Programming fix would need hcf for initial divides.
  n, n/Q%(1) > t = 166666666666667  2774956571.92965508problem # =9.   p(4)+prob = 4500000000000009  Repeat n1.

p(4)+prob..=4500000000000009= 3*3*3*166666666666667? Gap 59999 >60061^3 cofactor?
  Time speed,  sec = 10.7400000000000002
>>9  p(4)+prob..=4500000000000009= 3*3*3*166666666666667? Gap 59999 >60061^3 cofactor? 10s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000010 ****
4500000000000010=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  REM last factor         11
PROCf(X%)  REM last factor        787
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 227993 
progress  p(4)+prob..=4500000000000010= 2*5*11*787*  +(51981055793) ? more..
,,,
51981055793 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =10.   p(4)+prob = 4500000000000010  Repeat n1.

p(4)+prob..=4500000000000010= 2*5*11*787*51981055793prime
  Time speed,  sec = 29.7699999999999996
>>10  p(4)+prob..=4500000000000010= 2*5*11*787*51981055793prime 29s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000011 ****
4500000000000011=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  REM last factor         13
PROCf(X%)  REM last factor         31
PROCf(X%)  REM last factor         71
PROCf(X%)  REM last factor        337
PROCf(X%)  REM last factor      97367
 complete.

Unknown or missing variable at erl. 5440
problem # =11.   p(4)+prob = 4500000000000011  Repeat n1.

p(4)+prob..=4500000000000011= 13*31*71*337*4793*97367*all
  Time speed,  sec = 0.47999999999999998

>>11  p(4)+prob..=4500000000000011= 13*31*71*337*4793*97367*all 48cs

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000012 ****
4500000000000012=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  PROCf(X%)  REM last factor         23
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 4037864
progress  p(4)+prob..=4500000000000012= 2^2*3*23*  +(16304347826087) ? more..
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3243240, 4mn. <esc>
,,,,,,,,,,,,,,
16304347826087 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =12.   p(4)+prob = 4500000000000012  Repeat n1.

p(4)+prob..=4500000000000012= 2^2*3*23*16304347826087prime
  Time speed,  sec = 323.900000000000034
>>12  p(4)+prob..=4500000000000012= 2^2*3*23*16304347826087prime 5mn

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000013 ****
4500000000000013=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.9988464247527489
PROCf(X%)  REM last factor        521
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 2938917
progress  p(4)+prob..=4500000000000013= 521*  +(8637236084453) ? more..
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
8637236084453 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =13.   p(4)+prob = 4500000000000013  Repeat n1.

p(4)+prob..=4500000000000013= 521*8637236084453prime
  Time speed,  sec = 239.689999999999998
>>13  p(4)+prob..=4500000000000013= 521*8637236084453prime 3mn

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000014 ****
4500000000000014=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  REM last factor         17
PROCf(X%)  REM last factor         43
,,,,,,PROCf(X%)  REM last factor      11923
PROCf(X%)  REM last factor    6977147
 complete.

Unknown or missing variable at erl. 5440
problem # =14.   p(4)+prob = 4500000000000014  Repeat n1.

p(4)+prob..=4500000000000014= 2*17*37*43*11923*6977147*all
  Time speed,  sec = 2.24000000000000021
>>14  p(4)+prob..=4500000000000014= 2*17*37*43*11923*6977147*all 2s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000015 ****
4500000000000015=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  REM last factor          7
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 6546536
progress  p(4)+prob..=4500000000000015= 3*5*7*  +(42857142857143) ? more..

PROCf(X%)  REM last factor      95773
,
447486691 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =15.   p(4)+prob = 4500000000000015  Repeat n1.

p(4)+prob..=4500000000000015= 3*5*7*95773*447486691prime
  Time speed,  sec = 18.5199999999999996
>>15  p(4)+prob..=4500000000000015= 3*5*7*95773*447486691prime 18s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000016 ****
4500000000000016=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  PROCf(X%)  PROCf(X%)  REM last factor         41
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 486357 
progress  p(4)+prob..=4500000000000016= 2^2*2^2*29*41*  +(236543313709) ? more..
,,,,
PROCf(X%)  REM last factor     351347
,
673247 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =16.   p(4)+prob = 4500000000000016  Repeat n1.

p(4)+prob..=4500000000000016= 2^2*2^2*29*41*351347*673247prime
  Time speed,  sec = 38.5799999999999983
>>16  p(4)+prob..=4500000000000016= 2^2*2^2*29*41*351347*673247prime 38s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000017 ****
4500000000000017=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  REM last factor        277
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 4030569
progress  p(4)+prob..=4500000000000017= 277*  +(16245487364621) ? more..
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,3243240, 4mn. <esc>
,,,,,,,,,,,,,,
16245487364621 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =17.   p(4)+prob = 4500000000000017  Repeat n1.

p(4)+prob..=4500000000000017= 277*16245487364621prime
  Time speed,  sec = 331.379999999999996
>>17  p(4)+prob..=4500000000000017= 277*16245487364621prime 5mn

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000018 ****
4500000000000018=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 15811388         
progress  p(4)+prob..=4500000000000018= 2*3*3*  +(250000000000001) ? more..

cofactor too big.  Programming fix would need hcf for initial divides.
  n, n/Q%(1) > t = 250000000000001  4162434857.89449072problem # =18.   p(4)+prob = 4500000000000018  Repeat n1.

p(4)+prob..=4500000000000018= 2*3*3*250000000000001? Gap 59999 >60061^3 cofactor?
  Time speed,  sec = 10.4900000000000002
>>18  p(4)+prob..=4500000000000018= 2*3*3*250000000000001? Gap 59999 >60061^3 cofactor? 10s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000019 ****
4500000000000019=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  REM last factor         61
PROCf(X%)  REM last factor       1663
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 210617 
progress  p(4)+prob..=4500000000000019= 61*1663*  +(44359886833) ? more..
,,,
44359886833 ( is prime), repeat last factor enter n
  (5 beeps x 1sec.)
problem # =19.   p(4)+prob = 4500000000000019  Repeat n1.

p(4)+prob..=4500000000000019= 61*1663*44359886833prime
  Time speed,  sec = 29.6900000000000013
>>19  p(4)+prob..=4500000000000019= 61*1663*44359886833prime 29s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000020 ****
4500000000000020=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  REM last factor          5
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 15000000         
progress  p(4)+prob..=4500000000000020= 2^2*5*  +(225000000000001) ? more..

cofactor too big.  Programming fix would need hcf for initial divides.
  n, n/Q%(1) > t = 225000000000001  3746191372.10504341problem # =20.   p(4)+prob = 4500000000000020  Repeat n1.

p(4)+prob..=4500000000000020= 2^2*5*225000000000001? Gap 59999 >60061^3 cofactor?
  Time speed,  sec = 10.75
>>20  p(4)+prob..=4500000000000020= 2^2*5*225000000000001? Gap 59999 >60061^3 cofactor? 10s.

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?
p(4)+prob = 4.500E15   ****
p(4)+prob = 4500000000000021 ****
4500000000000021=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 51.998846424752756
PROCf(X%)  REM last factor         19
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
>? pmax. Gap? 60059
continue using test, to INT sqrn = 60061 - 2678998
progress  p(4)+prob..=4500000000000021= 3*11*19*  +(7177033492823) ? more..
,,,,,,,,,,,,,,,,,,,,,,,,,,,
Escape at erl. 5920
problem # =21.   p(4)+prob = 4500000000000021  Repeat n1.

p(4)+prob..=4500000000000021= 3*11*19*
  Time speed,  sec = 139.27000000000001
>>21  p(4)+prob..=4500000000000021= 3*11*19* 2mn

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?*

(Proc sumry).
spool. 1 = yes  (i.e. write output to ramdisk.sumryfact)



(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24. c241Q c22Byte 24-2-2003.)
limits 60013*60013*60017 bugs.  3^33+30 etc. = 3*47*549167*71792299.

my file > *ram.sumryfact.creditcd1..  Sun,02 Mar 2003.18:13:32
by don.mcdonald.pgm.c22Bc. BBC Basic64.Risc os.Acorn Archimedes comp 1990.

== LETTER values : C,A,T = 03,01,20. (BASE 100, Altern. base 27, keypad)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  2^52..=4503599627370496= Accy?(squ of(squ of(13th powof(2*all 5cs
3  45E15..=45000000000000000= Accy?(2^2*17*661764705882353? Gap 59999 >60061^3 cofactor? 10s.
4  45E14..=4500000000000000= 2^2*3*3*5*5*2^8*5*5*5*5*5*5*5*5*2^4*5*5*5*5*5*all 13cs
5  p(4)+prob..=4500000000000005= 5*1097*820419325433prime 1mn
6  p(4)+prob..=4500000000000006= 2*3*750000000000001? Gap 59999 >60061^3 cofactor? 10s.
7  p(4)+prob..=4500000000000007= 4500000000000007? Gap 59999 >60061^3 cofactor? 10s.
8  p(4)+prob..=4500000000000008= 2^2*7*2*47*131*5569*2343571*all 1s.
9  p(4)+prob..=4500000000000009= 3*3*3*166666666666667? Gap 59999 >60061^3 cofactor? 10s.
10  p(4)+prob..=4500000000000010= 2*5*11*787*51981055793prime 29s.
11  p(4)+prob..=4500000000000011= 13*31*71*337*4793*97367*all 48cs
continu.
12  p(4)+prob..=4500000000000012= 2^2*3*23*16304347826087prime 5mn
13  p(4)+prob..=4500000000000013= 521*8637236084453prime 3mn
14  p(4)+prob..=4500000000000014= 2*17*37*43*11923*6977147*all 2s.
15  p(4)+prob..=4500000000000015= 3*5*7*95773*447486691prime 18s.
16  p(4)+prob..=4500000000000016= 2^2*2^2*29*41*351347*673247prime 38s.
17  p(4)+prob..=4500000000000017= 277*16245487364621prime 5mn
18  p(4)+prob..=4500000000000018= 2*3*3*250000000000001? Gap 59999 >60061^3 cofactor? 10s.
19  p(4)+prob..=4500000000000019= 61*1663*44359886833prime 29s.
20  p(4)+prob..=4500000000000020= 2^2*5*225000000000001? Gap 59999 >60061^3 cofactor? 10s.
21  p(4)+prob..=4500000000000021= 3*11*19* 2mn
contin.

Summry. at erl. 1700
problem # =22.   * = 4500000000000021  Repeat n1.

p(4)+prob..=4500000000000021= 3*11*19*
  Time speed,  sec = 156.189999999999998
>>22  p(4)+prob..=4500000000000021= 3*11*19* 2mn

factor no. expr.  0, q.uit. +, datum  *, good summary reslts
  h, o help/ options   xx? poor

PLEASE ENTER)  numeric expression/no.,
?0
enter = close ,  or <ESC> resume.?
e n d. prog c241Q  24.2.03   close *spool
