>>  D.Pgms.maths.BigNum.sumr6e4p3
13.02.03  23:23
=======

(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24. c22Byte 13-2-2003.)
limits 60013*60013*60017 bugs.  3^33+30 etc. = 3*47*549167*71792299.

my file > *ram.sumryfact.creditcd1..  Thu,13 Feb 2003.23:16:40
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  60013*60013*60017   ..=216154836662873= 60013*60013*60017*all 19s.
3  3^33..=5559060566555523= Accy?(3th powof(11th powof(3*all 3cs
4  n1^2..=3.09031543826326114E31= Accy?(6th powof(11th powof(3*all 3cs
5  n1^2..=9.55004950796825132E62= Accy?( 34cs
6  n1^2..=9.12034456046446399E125= Accy?( 66cs
7  9.12034456046446399E..=9.12034456046446399E125= Accy?( 66cs
8  LNn1/LN3..=264= 2^3*3*11*all 3cs
9  3^264..=9.1203445604644655E125= Accy?(22th powof(3*3*3*3*3*3*3*3*3*3*3*3*all 5cs
10  3^264..=9.1203445604644655E125= Accy?(22th powof(3*3*3*3*3*3*3*3*3*3*3*3*all 51s.
11  3^264..=9.1203445604644655E125= Accy?(22th powof(3*3*3*3*3*3*3*3*3*3*3*3*all 1mn
continu.
12  R%(K1%)..=2147442871= 7*19*193*269*311*all 8cs
13  n1/7..=306777553= 19*193*269*311*all 8cs
14  n1/19..=16146187= 193*269*311*all 7cs
15  n1/269..=60023= 193*311*all 5cs
16  n1/269..=60023= 193*311*all 32s.
17  bet t lt(teleph kpd)..=238858= 2*119429*all 6cs
18  donald mcd(teleph kp..=366253623= 3*3*3*31*467*937*all 9cs
19  don s mcdonald (tele..=366762366253= 6361*57657973*all 2s.
contin.

Summry. at erl. 1700
problem # =20.   * = 366762366253  Repeat n1.

don s mcdonald (tele..=366762366253= 6361*57657973*all
  Time speed,  sec = 154.969999999999999
>>20  don s mcdonald (tele..=366762366253= 6361*57657973*all 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. close *spool

(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24. c22Byte 13-2-2003.)
limits 60013*60013*60017 bugs.  3^33+30 etc. = 3*47*549167*71792299.

my file > *ram.sumryfact.creditcd1..  Thu,13 Feb 2003.22:52:10
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  60013*60013*60017   ..=216154836662873= 60013*60013*60017*all 19s.
3  60013*60013*60017   ..=216154836662873= 60013*60013*60017*all 39s.
4  3^33+30..=5559060566555553= Accy?(3*47*549167*71792299prime 1mn
5  n1+2..=5559060566555555= Accy?(5*1111812113311111? Gap 59999 >60061^3 cofactor? 19s.
6  n1+2..=5559060566555557= Accy?(61*103*109*397*20446423*all 46cs
7  n1+2..=5559060566555559= Accy?(3*3*7*7*6073*2075675863*all 4s.
8  n1+2..=5559060566555561= Accy?(13*41*15187*17923*38317*all 5s.
9  n1+2..=5559060566555563= Accy?(101*233*1831*2803*46027*all 66cs
10  n1+2..=5559060566555565= Accy?(3*5*23753*29581*527447*all 7s.
11  p(1)..=216154836662873= 60013*60013*60017*all 19s.
continu.
12  3^33..=5559060566555523= Accy?(3th powof(11th powof(3*all 4cs
13  n1^2..=3.09031543826326114E31= Accy?(6th powof(11th powof(3*all 4cs
14  n1^2..=9.55004950796825132E62= Accy?( 16s.
15  n1^2..=9.55004950796825132E62= Accy?( 53s.
16  3^132..=9.55004950796825314E62= Accy?(11th powof(12th powof(3*all 4cs
17  3^135..=2.57851336715142822E64= Accy?(9th powof(15th powof(3*all 4cs
18  3^270..=6.64873118457859563E128= Accy?(15th powof(18th powof(3*all 5cs
19  3^540..=4.42056263647878971E257= Accy?(30th powof(3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*all 7cs
20  n1^(1/30)..=387420488.999999881= Accy?(2^3*7*13*19*37*757*all 6cs
21  INTn1+1..=387420489= squ of(3th powof(3th powof(3*all 3cs
contin.P

Summry. at erl. 1700
problem # =22.   * = 387420489  Repeat n1.

INTn1+1..=387420489= squ of(3th powof(3th powof(3*all
  Time speed,  sec = 78.0600000000000023
>>22  INTn1+1..=387420489= squ of(3th powof(3th powof(3*all 1mn

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

PLEASE ENTER)  numeric expression/no.,
?PI^540
PI^540 = 2.890E268  ****
PI^540 = 2.89022234823921911E268 ****
loss of Accuracy*** RESULTS will be WRONG. Contin.
loss of Accuracy*** RESULTS will be WRONG. Contin.
2.89022234823921911E268=  n > 2^31, not power.  try harder .. more 
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 891.807909915052164
nn/ X% =2.89022234823921911E268/2036934900  qy loss of precision? cont.

Floating point exception: invalid operation at erl. 6960
problem # =23.   PI^540 = 2.89022234823921911E268  Repeat n1.

PI^540..=2.89022234823921911E268= Accy?(
  Time speed,  sec = 3.70999999999999996
>>23  PI^540..=2.89022234823921911E268= Accy?( 3s.

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. close *spool

(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24.  6-2-2003.)
limits 46337*46349*46351 o.k.

my file > *ram.sumryfact.creditcd1..  Thu,13 Feb 2003.22:20:43
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  46337*46349*46351   ..=99546819636163= 46337*46349*46351*all 12s.
3  60061..=60061= 17*3533*all 4cs
4  n1-2..=60059= 19*29*109*all 4cs
5  n1-2..=60057= 3*3*6673*all 4cs
6  n1-2..=60055= 5*12011*all 4cs
7  n1-2..=60053= 7*23*373*all 4cs
8  n1-2..=60051= 3*37*541*all 4cs
9  n1-2..=60049= 11*53*103*all 4cs
10  n1-2..=60047= 13*31*149*all 4cs
11  n1-2..=60045= 3*5*4003*all 4cs
continu.
12  n1-2..=60043= 97*619*all 4cs
13  n1-2..=60041= 60041*all 5cs
14  n1-2..=60039= 3*3*7*953*all 4cs
15  n1-2..=60037= 60037*all 5cs
16  n1*p(13)^2..=216428682962197= 216428682962197? Gap 59999 >60061^3 cofactor? 19s.
17  60037..=60037= 60037*all 5cs
18  n1-2..=60035= 5*12007*all 4cs
19  n1-2..=60033= 3*20011*all 4cs
20  n1-2..=60031= 173*347*all 5cs
21  n1-2..=60029= 60029*all 5cs
22  n^2*p(17)..=216342179251117= 216342179251117? Gap 59999 >60061^3 cofactor? 19s.
23  p(21)..=60029= 60029*all 5cs
24  n1-2..=60027= 3*11*17*107*all 4cs
25  n1-2..=60025= squ of(5*7*7*all 3cs
26  n1-2..=60023= 193*311*all 5cs
27  n1-2..=60021= 3*3*3*3*3*13*19*all 4cs
28  n1-2..=60019= 47*1277*all 4cs
29  n1-2..=60017= 60017*all 5cs
30  n1-2..=60015= 3*5*4001*all 4cs
31  n1-2..=60013= 60013*all 5cs
continu.
32  n^2*p(29)..=216154836662873= 60013*60013*60017*all 19s.
33  n1+p3e4..=216154836722933= 233*349*2658175249prime 28s.
34  n1+p3e4..=216154836782993= 216154836782993? Gap 59999 >60061^3 cofactor? 19s.
35  n1+p3e4..=216154836843053= 8111*20287*1313629*all 5s.
36  n1+p3e4..=216154836903113= 83*2604275143411prime 2mn
37  n1+p3e4..=216154836963173= 131*1531*1077751093*all 2s.
38  n1+p3e4..=216154837023233= 103*1117*3271*574373*all 50cs
39  n1+p3e4..=216154837083293= 216154837083293? Gap 59999 >60061^3 cofactor? 19s.
40  n1+p3e4..=216154837143353= 216154837143353? Gap 59999 >60061^3 cofactor? 19s.
41  4E15+27..=4000000000000027= 31*31*137*24889*1220699*all 6s.
42  n1+30030..=4000000000030057= 4000000000030057? Gap 59999 >60061^3 cofactor? 19s.
43  n1+30030..=4000000000060087= 4000000000060087? Gap 59999 >60061^3 cofactor? 19s.
44  n1+30030..=4000000000090117= 23*257*1061*19583*32569*all 1s.
45  n1+30030..=4000000000120147= 673*5943536404339prime 3mn
46  n1+30030..=4000000000150177= 4000000000150177? Gap 59999 >60061^3 cofactor? 19s.
47  n1+30030..=4000000000180207= 4000000000180207? Gap 59999 >60061^3 cofactor? 19s.
48  10^27..=1.00000000000000001E27= Accy?(3th powof(3th powof(3th powof(2*5*all 3cs
49  10^28..=9.99999999999999958E27= Accy?(4th powof(7th powof(2*5*all 3cs
50  10^80..=1E80= Accy?(10th powof(2^8*5*5*5*5*5*5*5*5*all 6cs
51  10^81..=9.99999999999999921E80= Accy?(9th powof(9th powof(2*5*all 3cs
continu.
52  10^82..=9.99999999999999963E81= Accy?(41th powof(2^2*5*5*all 8cs
53  10^162..=9.99999999999999938E161= Accy?(18th powof(2^9*5*5*5*5*5*5*5*5*5*all 6cs
54  10^162..=9.99999999999999938E161= Accy?(18th powof(2^9*5*5*5*5*5*5*5*5*5*all 1mn
55  10^162..=9.99999999999999938E161= Accy?(18th powof(2^9*5*5*5*5*5*5*5*5*5*all 1mn
56  3^33..=5559060566555523= Accy?(3th powof(11th powof(3*all 4cs
57  n1+2..=5559060566555525= Accy?(5*5*222362422662221? Gap 59999 >60061^3 cofactor? 19s.
58  n1+2..=5559060566555527= Accy?(31*43*4170338009419prime 3mn
59  n1+2..=5559060566555529= Accy?(3*11*139*1211916408667prime 1mn
60  n1+2..=5559060566555531= Accy?(7*25307*31380705319prime 34s.
61  n1+2..=5559060566555533= Accy?(8663*641701554491prime 1mn
62  n1+2..=5559060566555535= Accy?(3*5*13*1213*2729*8611969*all 91cs
63  n1+2..=5559060566555537= Accy?(17*53*157*1669*23546189*all 75cs
64  n1+2..=5559060566555539= Accy?(811* 24s.
65  n1+2..=5559060566555541= Accy?(3*3*29*29*734451125189prime 1mn
66  n1+2..=5559060566555543= Accy?(5559060566555543? Gap 59999 >60061^3 cofactor? 19s.
67  n1+2..=5559060566555545= Accy?(5*7*23*79*2383*36682117*all 1s.
68  n1+2..=5559060566555547= Accy?(3*227*61547*132631721prime 24s.
69  n1+2..=5559060566555549= Accy?(19*37*37*229*2543*366997*all 32cs
70  n1+2..=5559060566555551= Accy?(11*757*797*837634429*all 1s.
71  n1+2..=5559060566555553= Accy?(3*47*549167*71792299prime 1mn
continu.
72  n1+2..=5559060566555555= Accy?(5*1111812113311111? Gap 59999 >60061^3 cofactor? 19s.
73  n1+2..=5559060566555557= Accy?(61*103*109*397*20446423*all 46cs
74  n1+2..=5559060566555559= Accy?(3*3*7*7*6073*2075675863*all 4s.
75  n1+2..=5559060566555561= Accy?(13*41*15187*17923*38317*all 5s.
76  n1+2..=5559060566555563= Accy?(101*233*1831*2803*46027*all 66cs
77  n1+2..=5559060566555565= Accy?(3*5*23753*29581*527447*all 8s.
78  n1+2..=5559060566555567= Accy?(6037*471673*1952267prime 56s.
79  n1+2..=5559060566555567= Accy?(6037*471673*1952267prime 1mn
80  P%(2*5760)..=60023= 193*311*all 5cs
81  R%(K1%)..=2147442871= 7*19*193*269*311*all 8cs
82  K1%..=7025= 5*5*281*all 4cs
83  R%(K1%-1)..=2147479820= 2^2*5*47*1277*1789*all 14cs
84  R%(K1%-2)..=2147468277= 3*11927*60017*all 76cs
85  n*n1..=128884603580709= 3*11927*60017*60017*all 19s.
86  R%(K1%+1)..=0= 1 (less than 2.) 1cs
87  p(85)..=128884603580709= 3*11927*60017*60017*all 19s.
88  n..=60017= 60017*all 5cs
89  n1-2..=60015= 3*5*4001*all 5cs
90  n1-2..=60013= 60013*all 6cs
91  n^2*p(88)..=216154836662873= 60013*60013*60017*all 19s.
continu.
contin.

Summry. at erl. 1700
problem # =92.   * = 216154836662873  Repeat n1.

n^2*p(88)..=216154836662873= 60013*60013*60017*all
  Time speed,  sec = 48.6700000000000017
>>92  n^2*p(88)..=216154836662873= 60013*60013*60017*all 48s.

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. close *spool


(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24.  6-2-2003.)
limits 46337*46349*46351 o.k.

my file > *ram.sumryfact.creditcd1..  Wed,12 Feb 2003.23:05:20
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  60061^2..=3607323721= squ of(17*3533*all 4cs
3  n1+2..=3607323723= 3*3*18713*21419*all 1s.
4  n1+2..=3607323725= 5*5*144292949*all 76cs
5  n1+2..=3607323727= 7*515331961*all 1s.
6  n1+2..=3607323729= 3*331*3632753*all 18cs
7  n1+2..=3607323731= 11*211*281*5531*all 9cs
8  n1+2..=3607323733= 13*3049*91009*all 25cs
9  n1+2..=3607323735= 3*5*12197*19717*all 78cs
10  n1+2..=3607323737= 23761*151817*all 6s.
11  n1+2..=3607323739= 3607323739prime 27s.


12  n1+2..=3607323741= 3*3*7*3*3*283*22481*all 9cs
13  n1+2..=3607323743= 47*76751569*all 59cs
14  n1+2..=3607323745= 5*199*673*5387*all 11cs
15  n1+2..=3607323747= 3*113*167*63719*all 9cs
16  n1+2..=3607323749= 23*443*354041*all 11cs
17  n1+2..=3607323751= 67*53840653*all 50cs
18  n1+2..=3607323753= 3*11*11*9937531*all 26cs
19  n1+2..=3607323755= 5*7*17*19*61*5231*all 8cs
20  n1+2..=3607323757= 821*4393817*all 33cs
21  n1+2..=3607323759= 3*3*13*13*2371679*all 16cs
22  n1+2..=3607323761= 4729*762809*all 1s.
23  n1+2..=3607323763= 3607323763prime 27s.
24  n1+2..=3607323765= 3*5*421*571231*all 12cs
25  n1+2..=3607323767= 71*2663*19079*all 24cs
26  n1+2..=3607323769= 7*37*2221*6271*all 20cs
27  n1+2..=3607323771= 3*1202441257*all 2s.
28  n1+2..=3607323773= 31*757*153719*all 12cs
29  n1+2..=3607323775= 5*5*11*29*452329*all 11cs
30  n1+2..=3607323777= 3*3*101*3968453*all 19cs
31  n1+2..=3607323779= 59*1759*34759*all 19cs


32  n1+2..=3607323781= 3607323781prime 27s.
33  n1+2..=3607323783= 3*7*103*1667741*all 15cs
34  n1+2..=3607323785= 5*13*97*572137*all 12cs
35  n1+2..=3607323787= 41*87983507*all 62cs
36  n1+2..=3607323789= 3*17*53*1334563*all 14cs
37  n1+2..=3607323791= 13457*268063*all 3s.
38  n1+2..=3607323793= 19*43*4415329*all 20cs
39  n1+2..=3607323795= 3*3*5*3*23*239*4861*all 9cs
40  n1+2..=3607323797= 7*7*11*7*577*1657*all 11cs
41  n1+2..=3607323799= 3607323799prime 27s.
42  n1+2..=3607323801= 3*33863*35509*all 2s.
43  n1+2..=3607323803= 7019*513937*all 1s.
44  n1+2..=3607323805= 5*1033*698417*all 13cs
45  n1+2..=3607323807= 3*1202441269*all 2s.
46  n1+2..=3607323809= 3779*954571*all 98cs
47  n1+2..=3607323811= 7*13*39640921*all 44cs
48  n1+2..=3607323813= 3*3*131*179*17093*all 9cs
49  n1+2..=3607323815= 5*721464763*all 1s.
50  n1+2..=3607323817= 3607323817prime 27s.
51  n1+2..=3607323819= 3*11*1291*84673*all 15cs


52  n1+2..=3607323821= 193*18690797*all 35cs
53  n1+2..=3607323823= 17*149*163*8737*all 8cs
54  n1+2..=3607323825= 3*5*5*7*337*20389*all 9cs
55  n1+2..=3607323827= 16417*219731*all 4s.
56  n1+2..=3607323829= 3547*1017007*all 92cs
57  n1+2..=3607323831= 3*3*19*21095461*all 34cs
58  n1+2..=3607323833= 29*79*1574563*all 15cs
59  n1+2..=3607323835= 5*31*73*318809*all 11cs
60  n1+2..=3607323837= 3*13*47*727*2707*all 12cs
61  n1+2..=3607323839= 7*83*6208819*all 22cs
62  n1+2..=3607323841= 11*23*1039*13723*all 14cs
63  n1+2..=3607323843= 3*37*32498413*all 40cs
64  n1+2..=3607323845= 5*157*1451*3167*all 16cs
65  n1+2..=3607323847= 137*26330831*all 39cs
66  n1+2..=3607323849= 3*3*3*107*1248641*all 14cs
67  n1+2..=3607323851= 57331*62921*all 17s.     ***

68  n*n1..=226976424028771= 57331*62921*62921*1prime 24s.  good
69  n1+2..=226976424028773= 3*1499*52127*968267*all 14s.    good
70  n1+2..=226976424028775= 5*5*67*1607*84323779*all 93cs
71  n1+2310..=226976424031085= 5*31*43*137*248576477*all 1s.


72  n1+2..=226976424031087= 226976424031087? Gap 59999 
>60061^3 cofactor? 19s.
73  n1+p3e4..=226976424091147= 79*179*16050945767prime 32s.   ??
74  n1+p3e4..=226976424151207= 226976424151207? Gap 59999 
>60061^3 cofactor? 19s.
75  n1+p3e4..=226976424211267= 226976424211267? Gap 59999 
>60061^3 cofactor? 19s.
76  n1+p3e4..=226976424271327= 226976424271327? Gap 59999 
>60061^3 cofactor? 19s.
77  n1+p3e4..=226976424331387= 419*143947*3763259prime 30s. good
78  n1+p3e4..=226976424391447= 59*3847058040533prime 2mn
79  n1+p3e4..=226976424451507= 31*479*36497*418819*all 9s.
80  n1+p3e4..=226976424511567= 43*193*277*439*224911*all 18cs
81  n1+p3e4..=226976424571627= 19*3559*3356596687prime 28s.
82  n1+p3e4..=226976424631687= 101*1061*2118087967*all 2s.
83  n1+p3e4..=226976424691747= 23*181*54522321569prime 37s.
84  n1+p3e4..=226976424751807= 226976424751807? Gap 59999 
>60061^3 cofactor? 19s.
85  n1+p3e4..=226976424811867= 226976424811867? Gap 59999 
>60061^3 cofactor? 19s.
86  n1+p3e4..=226976424871927= 17*3023*4416657097prime 28s.



Summry. at erl. 1700
problem # =87.   * = 226976424871927  Repeat n1.

n1+p3e4..=226976424871927= 17*3023*4416657097prime
  Time speed,  sec = 219.640000000000015
>>87  n1+p3e4..=226976424871927= 17*3023*4416657097prime 3mn

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

PLEASE ENTER)  numeric expression/no.,
?0
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(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24.  6-2-2003.)
limits 46337*46349*46351 o.k.

my file 
> *ram.sumryfact.creditcd1..  Wed,12 Feb 2003.01:31:21
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  46337*46349*46351   ..=99546819636163= 46337*46349*46351*all 12s. easy
3  60061..=60061= 17*3533*all 4cs
4  n1-2..=60059= 19*29*109*all 4cs
5  n1-2..=60057= 3*3*6673*all 4cs
6  n1-2..=60055= 5*12011*all 4cs
7  n1-2..=60053= 7*23*373*all 4cs
8  n1-2..=60051= 3*37*541*all 4cs
9  n1-2..=60049= 11*53*103*all 4cs
10  n1-2..=60047= 13*31*149*all 4cs
11  n1-2..=60045= 3*5*4003*all 4cs

12  n1-2..=60043= 97*619*all 4cs
13  n1-2..=60041= 60041*all 5cs            prime
14  n1-2..=60039= 3*3*7*953*all 4cs
15  n1-2..=60037= 60037*all 5cs            prime
16  n^2*60041..=216414264236129= 216414264236129? Gap 59999   BUG XX
>60061^3 cofactor? 19s.     no xxx.
17  59999..=59999= 59999*all 5cs           prime
18  n1-2..=59997= 3*7*2857*all 4cs
19  n1-2..=59995= 5*13*13*71*all 4cs
20  n1-2..=59993= 17*3529*all 4cs
21  n1-2..=59991= 3*19997*all 5cs
22  n1-2..=59989= 239*251*all 5cs
23  n1-2..=59987= 223*269*all 5cs
24  n1-2..=59985= 3*3*5*31*43*all 4cs
25  n1-2..=59983= 7*11*19*41*all 4cs
26  n1-2..=59981= 59981*all 5cs            prime
27  n^2*p(17)..=215859623939639= 59981*59981*59999*all 19s. good.
28  n+2..=60001= 29*2069*all 4cs
29  n1+2..=60003= 3*3*59*113*all 4cs
30  n1+2..=60005= 5*11*1091*all 4cs
31  n1+2..=60007= 23*2609*all 4cs

32  n1+2..=60009= 3*83*241*all 4cs
33  n1+2..=60011= 7*8573*all 4cs
34  n1+2..=60013= 60013*all 5cs
35  n^2*59999..=216090008579831= 59999*60013*60013*all 19s. good
36  n..=60013= 60013*all 5cs          last prime factor
37  n1+2..=60015= 3*5*4001*all 4cs
38  n1+2..=60017= 60017*all 5cs          prime
39  n^2*p(36)..=216169243863757= 60013*60017*60017*all 19s. good
40  n..=60017= 60017*all 5cs
41  n1+2..=60019= 47*1277*all 4cs
42  n1+2..=60021= 3*3*3*3*3*13*19*all 4cs
43  n1+2..=60023= 193*311*all 5cs
44  n1+2..=60025= squ of(5*7*7*all 3cs
45  n1+2..=60027= 3*11*17*107*all 4cs
46  n1+2..=60029= 60029*all 5cs
47  n^2*p(40)..=216270109634297= 60017*3603480841prime 28s. bug xx
48  n..=3603480841= squ of(60029*all 5cs
49  n+2..=60031= 173*347*all 5cs
50  60029..=60029= 60029*all 5cs
51  n1+2..=60031= 173*347*all 5cs

52  n1+2..=60033= 3*20011*all 4cs
53  n1+2..=60035= 5*12007*all 4cs
54  n1+2..=60037= 60037*all 5cs        prime
55  n^2*p(50)..=216371010939701= 216371010939701? Gap 59999 xx bug
>60061^3 cofactor? 19s.
57  RND(606)*2*3*5*7*11*..=467506502493209= 467506502493209? Gap 59999 
>60061^3 cofactor? 19s.
58  RND(606)*2*3*5*7*11*..=3873625306370903= 3873625306370903? Gap 59999 
>60061^3 cofactor? 19s.
59  RND(606)*2*3*5*7*11*..=2226221440443047= 743*3359*19709*45259*all 2s.
good
60  RND(606)*2*3*5*7*11*..=1024061862603971= 8609*118952475619prime 47s. ??
61  n..=118952475619= 118952475619prime 47s.
62  2^51..=2251799813685248= 3th powof(17th powof(2*all 5cs
63  n1..=2251799813685248= 3th powof(17th powof(2*all 5cs
64  d+P%(prob-60)..=2251799813685253= 13*2927*146423*404161prime 31s. xx

very good?
65  d+P%(prob-60)..=2251799813685255= 3*5*19*7901051977843prime 3mn
66  d+P%(prob-60)..=2251799813685259= 2251799813685259? Gap 59999 
>60061^3 cofactor? 19s.
67  d+P%(prob-60)..=2251799813685261= 3*7* 1mn
68  n1/21..=107228562556441=  31s.    interrupt.
69  d+P%(prob-60)..=2251799813685267= 3*3*29*2027*4256332261prime 28s.
70  n..=4256332261= 4256332261prime 28s.
71  d+P%(prob-60)..=2251799813685277= 31* 3mn

72  d+P%(prob-60)..=2251799813685279= 3*11*13*707159*7422589prime 1mn
very good
73  d+P%(prob-60)..=2251799813685285= 3*3*5*3* 2mn

Summry. at erl. 1700
problem # =74.   * = 2251799813685285  Repeat n1.

d+P%(prob-60)..=2251799813685285= 3*3*5*3*
  Time speed,  sec = 214.849999999999994
>>74  d+P%(prob-60)..=2251799813685285= 3*3*5*3* 3mn

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. close *spool


(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)
(higher filtering of primes. ?? prog c24.  6-2-2003.)
limits 46337*46349*46351 o.k.

my file > *ram.sumryfact.creditcd1..  Tue,11 Feb 2003.23:47:56
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  46337*46349*46351   ..=99546819636163= 46337*46349*46351*all 12s.
3  59001..=59001= 3*71*277*all 4cs
4  n1-2..=58999= 41*1439*all 4cs
5  n1-2..=58997= 58997*all 5cs
6  n1-2..=58995= 3*3*3*5*19*23*all 4cs
7  n1-2..=58993= 11*31*173*all 4cs
8  n1-2..=58991= 58991*all 5cs
9  n*p(5)..=3480292027= 58991*58997*all 18s.
10  n*n1..=205326788716919= 58991*58997*58997*all 18s.
11  n-2..=58995= 3*3*3*5*19*23*all 4cs

15  p(10)..=205326788716919= 58991*58997*58997*all 18s.
16  n+2..=58999= 41*1439*all 4cs
17  n1+2..=59001= 3*71*277*all 5cs
18  n1+2..=59003= 7*8429*all 5cs
19  n1+2..=59005= 5*11801*all 5cs
20  n1+2..=59007= 3*13*17*89*all 4cs
21  n1+2..=59009= 59009*all 5cs
22  n1+2..=59011= 59011*all 5cs
23  n^2*p(21)..=205486929822089= 59009*59011*59011*all 18s.
24  n+2..=59013= 3*3*79*83*all 5cs
25  n1+2..=59015= 5*11*29*37*all 4cs
26  n1+2..=59017= 7*8431*all 5cs
27  n1+2..=59019= 3*103*191*all 5cs
28  n1+2..=59021= 59021*all 5cs
29  n1+2..=59023= 59023*all 5cs
30  n^2*p(28)..=205612315216109= 59021*59023*59023*all 18s.
31  n+2..=59025= 3*5*5*787*all 4cs

32  n1+2..=59027= 67*881*all 4cs
33  n1+2..=59029= 59029*all 5cs
34  n1+2..=59031= 3*3*7*937*all 4cs
35  n1+2..=59033= 13*19*239*all 4cs
36  n1+2..=59035= 5*11807*all 5cs
37  n1+2..=59037= 3*11*1789*all 4cs
38  n1+2..=59039= 43*1373*all 4cs
39  n1+2..=59041= 17*23*151*all 4cs
40  n1+2..=59043= 3*19681*all 5cs
41  n1+2..=59045= 5*7*7*241*all 4cs
42  n1+2..=59047= 137*431*all 5cs
43  n1+2..=59049= squ of(5th powof(3*all 3cs
44  n1+2..=59051= 59051*all 5cs
45  n^2*p(33)..=205835339056429= 59029*59051*59051*all 18s.
46  n+2..=59053= 59053*all 5cs
47  n1+2..=59055= 3*5*31*127*all 4cs
48  n1+2..=59057= 73*809*all 5cs
49  n1+2..=59059= 7*11*13*59*all 4cs
50  n1+2..=59061= 3*19687*all 5cs
51  n1+2..=59063= 59063*all 5cs

52  n1+2..=59065= 5*11813*all 5cs
53  n1+2..=59067= 3*3*6563*all 5cs
54  n1+2..=59069= 59069*all 5cs
55  n^2*p(51)..=206079475144943= 59063*59069*59069*all 18s.

56  10^prob..=1.00000000000000009E56= Accy?(7th powof(8th powof(2*5*all 4cs
57  10^prob..=1.00000000000000005E57= Accy?(19th powof(2^3*5*5*5*all 5cs
rem finds a power of integer, does not realise that integer is also a cube xx
it needs to try all powers again.

58  10^prob..=9.99999999999999944E57= Accy?(29th powof(2^2*5*5*all 7cs
59  10^prob..=9.99999999999999972E58= Accy?(59th powof(2*5*all 11cs
60  10^prob..=9.99999999999999949E59= Accy?(10th powof(2^6*5*5*5*5*5*5*all 5cs
61  10^prob..=9.99999999999999949E60= Accy?(61th powof(2*5*all 12cs
62  10^prob..=1.00000000000000004E62= Accy?(31th powof(2^2*5*5*all 7cs
63  10^prob..=1.00000000000000006E63= Accy?(7th powof(9th powof(2*5*all 4cs
64  10^prob..=1.00000000000000002E64= Accy?(8th powof(8th powof(2*5*all 4cs
65  10^prob..=9.99999999999999992E64= Accy?(13th powof(2^5*5*5*5*5*5*all 5cs
66  10^prob..=9.99999999999999945E65= Accy?(11th powof(2^6*5*5*5*5*5*5*all 5cs
67  10^prob..=9.99999999999999983E66= Accy?(67th powof(2*5*all 13cs
68  10^prob..=9.99999999999999953E67= Accy?(17th powof(2^4*5*5*5*5*all 5cs
69  10^prob..=1.00000000000000007E69= Accy?(23th powof(2^3*5*5*5*all 6cs

70  10^(3*prob+1)..=9.99999999999999956E210= Accy?(211th powof(2*5*all 35cs
71  10^(3*prob+1)..=9.99999999999999955E213= Accy?(107th powof(2^2*5*5*all 19cs

72  10^(3*prob+1)..=9.9999999999999996E216= Accy?(31th powof(2^7*5*5*5*5*5*5*5*all 7cs
73  10^(3*prob+1)..=9.99999999999999997E219= Accy?(44th powof(2^5*5*5*5*5*5*all 9cs
74  10^(3*prob+1)..=1.00000000000000005E223= Accy?(223th powof(2*5*all 37cs
75  10^(3*prob+1)..=9.99999999999999961E225= Accy?(113th powof(2^2*5*5*all 20cs
76  10^(3*prob+1)..=9.99999999999999992E228= Accy?(229th powof(2*5*all 38cs
77  10^(3*prob+1)..=1.00000000000000006E232= Accy?(29th powof(2^8*5*5*5*5*5*5*5*5*all 7cs
78  10^(3*prob+1)..=1.00000000000000005E235= Accy?(47th powof(2^5*5*5*5*5*5*all 9cs
79  10^(3*prob+1)..=1.00000000000000005E238= Accy?(34th powof(2^7*5*5*5*5*5*5*5*all 8cs
80  10^(3*prob+1)..=1.00000000000000005E241= Accy?(241th powof(2*5*all 40cs
81  10^(3*prob+1)..=1.00000000000000008E244= Accy?(61th powof(2^4*5*5*5*5*all 12cs
82  10^(3*prob+1)..=9.99999999999999952E246= Accy?(247th powof(2*5*all 41cs
83  10^(3*prob+1)..=9.99999999999999921E249= Accy?(50th powof(2^5*5*5*5*5*5*all 10cs
84  10^(3*prob+1)..=9.99999999999999936E252= Accy?(253th powof(2*5*all 42cs
85  10^(3*prob+1)..=1.00000000000000003E256= Accy?(32th powof(2^8*5*5*5*5*5*5*5*5*all 7cs
86  10^(3*prob+1)..=9.99999999999999929E258= Accy?(37th powof(2^7*5*5*5*5*5*5*5*all 8cs
87  10^(3*prob+1)..=1.00000000000000002E262= Accy?(131th powof(2^2*5*5*all 22cs
88  10^(3*prob+1)..=1.00000000000000007E265= Accy?(53th powof(2^5*5*5*5*5*5*all 11cs
89  10^(3*prob+1)..=9.99999999999999974E267= Accy?(67th powof(2^4*5*5*5*5*all 13cs
90  10^(3*prob+1)..=9.99999999999999953E270= Accy?(271th powof(2*5*all 44cs
91  10^(3*prob+1)..=9.99999999999999922E273= Accy?(137th powof(2^2*5*5*all 23cs

92  10^(3*prob+1)..=1E277= Accy?(277th powof(2*5*all 45cs
93  10^(3*prob+1)..=1.00000000000000003E280= Accy?(35th powof(2^8*5*5*5*5*5*5*5*5*all 8cs
94  10^(3*prob+1)..=9.99999999999999956E282= Accy?(283th powof(2*5*all 46cs
95  10^(3*prob+1)..=1.00000000000000003E286= Accy?(143th powof(2^2*5*5*all 24cs
96  10^(3*prob+1)..=1.00000000000000006E289= Accy?(289th powof(2*5*all 47cs
97  10^(3*prob+1)..=1.00000000000000001E292= Accy?(73th powof(2^4*5*5*5*5*all 13cs
98  10^(3*prob+1)..=9.99999999999999982E294= Accy?(59th powof(2^5*5*5*5*5*5*all 11cs
99  10^(3*prob+1)..=9.9999999999999996E297= Accy?(149th powof(2^2*5*5*all 25cs
100  10^(3*prob+1)..=1.00000000000000005E301= Accy?(43th powof(2^7*5*5*5*5*5*5*5*all 9cs
101  10^(3*prob+1)..=9.9999999999999994E303= Accy?(38th powof(2^8*5*5*5*5*5*5*5*5*all 8cs
102  10^(3*prob+1)..=9.99999999999999986E306= Accy?(307th powof(2*5*all 50cs


error floating point exceeded .. etc.
103  10^(3*prob+1)..=9.99999999999999986E306= Accy?(307th powof(2*5*all 9s.
104  10^(3*prob+1)..=9.99999999999999986E306= Accy?(307th powof(2*5*all 1mn

105  6E4+1..=60001= 29*2069*all 4cs
106  n1+2..=60003= 3*3*59*113*all 4cs
107  n1+2..=60005= 5*11*1091*all 4cs
108  n1+2..=60007= 23*2609*all 4cs
109  n1+2..=60009= 3*83*241*all 5cs
110  n1+2..=60011= 7*8573*all 5cs
111  n1+2..=60013= 60013*all 5cs

112  n1+2..=60015= 3*5*4001*all 4cs
113  n1+2..=60017= 60017*all 5cs
114  n*p(111)..=3601800221= 3601800221? >1^3 cofactor? 18s.

bug partly fixed 12.02.03.

115  RND(606)*2*3*5*7*11*..=3673265376730987= 37*99277442614351? 
bug  >1^3 cofactor? 19s.
116  RND(606)*2*3*5*7*11*..=1231842530378557= 1231842530378557? 
bug  >1^3 cofactor? 19s.
117  RND(606)*2*3*5*7*11*..=2916350086980353= 23*277*17519*26128997*all 4s.
118  RND(606)*2*3*5*7*11*..=3502588399630499= 5939*589760633041? 
bug  >1^3 cofactor? 19s.
119  RND(606)*2*3*5*7*11*..=4036881545336753= 1901*43987*48276919*all 11s.
120  RND(606)*2*3*5*7*11*..=2122331106555809= 43*71*547*1270863799*all 2s.
121  RND(606)*2*3*5*7*11*..=29682952539347= 83*357625934209? 
bug  >1^3 cofactor? 19s.

Summry. at erl. 1700
problem # =122.   * = 29682952539347  Repeat n1.

RND(606)*2*3*5*7*11*..=29682952539347= 83*357625934209? 
bug  >1^3 cofactor?
  Time speed,  sec = 28.4000000000000021
>>122  RND(606)*2*3*5*7*11*..=29682952539347= 83*357625934209?
bug  >1^3 cofactor? 28s.

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. close *spool
