
(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)

(higher filtering of primes. ??  4-2-2003.)

my file > *ram.sumryfact.creditcd1..  Thu,06 Feb 2003.19:08:51
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)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  2^51+P%(prob)..=2251799813685259= 2251799813685259? >46201^3 cofactor? 7s.
3  2^51+P%(prob)..=2251799813685261= 3*7*107228562556441? >46201^3 cofactor? 7s.
4  2^51+P%(prob)..=2251799813685265= 5*467*3433*280911223*all 1s.
5  2^51+P%(prob)..=2251799813685267= 3*3*29*2027*4256332261prime 14s.
6  2^51+P%(prob)..=2251799813685271= 2251799813685271? >46201^3 cofactor? 7s.
7  2^51+P%(prob)..=2251799813685277= 31* 2mn
8  5*2^49..=2814749767106560= 2^5*5*2^5*2^20*2^19*all 8cs
9  2^47..=140737488355328= 47th powof(2*all 4cs
10  2^49..=562949953421312= 7th powof(7th powof(2*all 2cs
11  n1+2..=562949953421314= 2*193*65537*22253377prime 14s.
continu.
12  5^5*11^6..=5536128125= 5*11*5*5*5*5*11*11*11*11*11*all 6cs


23  prob..=23= 23*all 5cs
24  prob..=24= 2^3*3*all 5cs
25  prob..=25= squareof(5*all 2cs
26  prob..=26= 2*13*all 5cs
27  prob..=27= 3th powof(3*all 2cs
28  prob..=28= 2^2*7*all 5cs
29  prob..=29= 29*all 5cs
30  prob..=30= 2*3*5*all 5cs
31  prob..=31= 31*all 5cs
continu.
32  prob..=32= 5th powof(2*all 2cs
33  prob..=33= 3*11*all 5cs
34  prob..=34= 2*17*all 5cs
35  prob..=35= 5*7*all 5cs
36  prob..=36= squareof(2*3*all 2cs
37  prob..=37= 37*all 5cs
38  prob..=38= 2*19*all 5cs
39  prob..=39= 3*13*all 5cs
40  prob..=40= 2^3*5*all 5cs
41  prob..=41= 41*all 5cs
42  prob..=42= 2*3*7*all 5cs
43  prob..=43= 43*all 5cs
44  prob..=44= 2^2*11*all 5cs
45  prob..=45= 3*3*5*all 5cs
46  prob..=46= 2*23*all 5cs
47  prob..=47= 47*all 5cs
48  prob..=48= 2^4*3*all 5cs
49  prob..=49= squareof(7*all 2cs
50  prob..=50= 2*5*5*all 5cs
51  prob..=51= 3*17*all 5cs
continu.
52  prob..=52= 2^2*13*all 5cs

53  prob^2*(prob+1)^3..=442316376= 2^3*3*3*3*3*3*3*3*3*3*53*53*all 6cs
54  prob^2*(prob+1)^3..=485149500= 2^2*3*3*3*3*3*3*5*5*5*11*11*11*all 6cs
55  prob^2*(prob+1)^3..=531238400= 2^9*5*5*7*7*7*11*11*all 6cs
56  prob^2*(prob+1)^3..=580765248= 2^6*3*3*3*7*7*19*19*19*all 5cs
57  prob^2*(prob+1)^3..=633918888= 2^3*3*3*19*19*29*29*29*all 6cs
58  prob^2*(prob+1)^3..=690894956= 2^2*29*29*59*59*59*all 6cs
59  prob^2*(prob+1)^3..=751896000= 2^6*3*3*3*5*5*5*59*59*all 6cs
60  prob^2*(prob+1)^3..=817131600= 2^4*3*3*5*5*61*61*61*all 6cs
61  prob^2*(prob+1)^3..=886818488= 2^3*31*31*31*61*61*all 6cs
62  prob^2*(prob+1)^3..=961180668= 2^2*3*3*3*3*3*3*7*7*7*31*31*all 6cs
63  prob^2*(prob+1)^3..=1040449536= squareof(2^9*3*3*7*all 6cs
64  prob^2*(prob+1)^3..=1124864000= 3th powof(2^4*5*13*all 5cs
65  prob^2*(prob+1)^3..=1214670600= 2^3*3*3*3*5*5*11*11*11*13*13*all 6cs
66  prob^2*(prob+1)^3..=1310123628= 2^2*3*3*11*11*67*67*67*all 6cs
67  prob^2*(prob+1)^3..=1411485248= 2^6*17*17*17*67*67*all 6cs
68  prob^2*(prob+1)^3..=1519025616= 2^4*3*3*3*17*17*23*23*23*all 6cs
69  prob^2*(prob+1)^3..=1633023000= 2^3*3*3*5*5*5*7*7*7*23*23*all 6cs
70  prob^2*(prob+1)^3..=1753763900= 2^2*5*5*7*7*71*71*71*all 6cs
71  prob^2*(prob+1)^3..=1881543168= 2^9*3*3*3*3*3*3*71*71*all 6cs
continu.
72  prob^2*(prob+1)^3..=2016664128= 2^6*3*3*3*3*73*73*73*all 6cs
73  prob^2*(prob+1)^3..=2159438696= 2^3*37*37*37*73*73*all 7cs
74  prob^2*(prob+1)^3..=2310187500= 2^2*3*5*3*3*5*5*5*5*5*37*37*all 7cs
75  prob^2*(prob+1)^3..=2469240000= 2^5*3*5*19*2*3*5*5*5*19*19*all 7cs
76  prob^2*(prob+1)^3..=2636934608= 2^4*7*11*19*7*7*11*11*19*all 6cs
77  prob^2*(prob+1)^3..=2813618808= 2^3*3*7*11*13*13*3*3*7*11*13*all 6cs
78  prob^2*(prob+1)^3..=2999649276= 2^2*3*13*13*3*79*79*79*all 7cs
79  prob^2*(prob+1)^3..=3195392000= 2^5*5*2^7*5*5*79*79*all 7cs
80  prob^2*(prob+1)^3..=3401222400= squareof(2^4*3*3*3*3*3*3*5*all 5cs
81  prob^2*(prob+1)^3..=3617525448= 2^3*3*3*3*3*3*3*3*3*41*41*41*all 6cs
82  prob^2*(prob+1)^3..=3844695788= 2^2*41*41*83*83*83*all 6cs
83  prob^2*(prob+1)^3..=4083137856= 2^5*3*7*2*3*3*7*7*83*83*all 7cs
84  prob^2*(prob+1)^3..=4333266000= 2^4*3*5*7*17*3*5*5*7*17*17*all 7cs
85  prob^2*(prob+1)^3..=4595504600= 2^3*5*17*5*17*43*43*43*all 7cs
86  prob^2*(prob+1)^3..=4870288188= 2^2*3*3*3*29*29*29*43*43*all 6cs
87  prob^2*(prob+1)^3..=5158061568= 2^5*3*11*2^4*3*11*11*29*29*all 7cs
88  prob^2*(prob+1)^3..=5459279936= 2^5*11*2*11*89*89*89*all 7cs
89  prob^2*(prob+1)^3..=5774409000= 2^3*3*5*3*3*3*3*3*5*5*89*89*all 7cs
90  prob^2*(prob+1)^3..=6103925100= 2^2*3*5*7*13*13*3*3*3*5*7*7*13*all 7cs
91  prob^2*(prob+1)^3..=6448315328= 2^5*7*13*13*2*7*23*23*23*all 6cs
continu.
92  prob^2*(prob+1)^3..=6808077648= 2^4*3*3*3*23*23*31*31*31*all 6cs
93  prob^2*(prob+1)^3..=7183721016= 2^3*3*3*31*31*47*47*47*all 7cs
94  prob^2*(prob+1)^3..=7575765500= 2^2*5*19*5*5*19*19*47*47*all 7cs
95  prob^2*(prob+1)^3..=7984742400= 2^5*3*5*19*2^10*3*3*5*19*all 7cs
96  prob^2*(prob+1)^3..=8411194368= 2^5*3*2^5*3*97*97*97*all 6cs
97  prob^2*(prob+1)^3..=8855675528= 2^3*7*7*7*7*7*7*97*97*all 7cs
98  prob^2*(prob+1)^3..=9318751596= 2^2*3*7*11*3*3*3*3*3*7*7*7*11*11*all 7cs
99  prob^2*(prob+1)^3..=9801000000= squareof(2^3*3*3*5*5*5*11*all 6cs
100  prob^2*(prob+1)^3..=10303010000= 2^4*5*5*5*5*101*101*101*all 7cs
101  prob^2*(prob+1)^3..=10825382808= 2^3*3*17*3*3*17*17*101*101*all 7cs
102  prob^2*(prob+1)^3..=11368731708= 2^2*3*17*3*17*103*103*103*all 7cs
103  prob^2*(prob+1)^3..=11933682176= 2^5*13*13*2^4*13*103*103*all 7cs
104  prob^2*(prob+1)^3..=12520872000= 2^5*3*5*7*13*13*2*3*3*5*5*7*7*all 7cs
105  prob^2*(prob+1)^3..=13130951400= 2^3*3*5*7*3*5*7*53*53*53*all 7cs
106  prob^2*(prob+1)^3..=13764583148= 2^2*53*53*107*107*107*all 8cs
107  prob^2*(prob+1)^3..=14422442688= 2^5*3*2*3*3*3*3*3*3*3*3*107*107*all 7cs
108  prob^2*(prob+1)^3+1..=15105218257= 1913*7896089*all 49cs
109  prob^2*(prob+1)^3+1..=15813611001= 3* 35s.
110  n1..=15813611001= 3* 42s.    BUG FIXED  06.02.03  22:10
111  n1..=15813611001= 3* 1mn     BUG FIXED  06.02.03  22:10
continu.
112  n1..=5271203667= 3*2963*593003*all 22cs


n1..=5271203667= 3*2963*593003*all
  Time speed,  sec = 51.3999999999999986
>>113  n1..=5271203667= 3*2963*593003*all 51s.

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

PLEASE ENTER)  numeric expression/no.,
 or  C= 8xCAP letr word(base 100, Z base 27) Ppt= teleph keypad 
n,n1,d (may refer to last factor n/test n1/ or Datum, d)
 e.g. n1+30.  p()=previous prob/ value , P%() prime , R%() primorial.
r.andom test =r,  or
<CR>,  very easy (a)gain,  repeat similar formula.?15813611001

15813611001 = 1.581E10   ****
15813611001 = 15813611001 ****
PROCtest.  for numbers larger than BASIC INTEger limit
= 2^ 33.8804477902190655

110  n1..=15813611001= 3* 42s.    BUG FIXED  06.02.03  22:10

Escape at erl. 4420
problem # =114.   15813611001 = 15813611001  Repeat n1.

15813611001..=15813611001= 3*
  Time speed,  sec = 14.9199999999999999
>>114  15813611001..=15813611001= 3* 14s.

(factor credit card numbers.  **continued fraction? method  2^52=4.5E15)

(higher filtering of primes. ??  4-2-2003.)

my file > *ram.sumryfact.creditcd1..  Thu,06 Feb 2003.18:46:28
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)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  2^48+1  example...=2.814749767E14= Accy?(squareof(squareof(squareof(squareof(3th powof(2*all 2cs
3  2^48+1  example...=2.814749767E14= Accy?(squareof(squareof(squareof(squareof(3th powof(2*all 2cs
4  RND(2E9)..=1718127463= 13*101*1308551*all 9cs
5  RND(2E9)..=527304173= 11*173*401*691*all 5cs
6  RND(2E9)..=1346871271= 251*5366021*all 14cs
7  RND(2E9)..=1984824154= 2*17*1453*40177*all 10cs
8  RND(2E9)..=1357505123= 13*104423471*all 55cs
9  RND(2E9)..=1270381331= 1270381331*all 1s.
10  RND(2E9)..=521855750= 2*5*5*5*13*211*761*all 4cs
11  RND(2E9)..=1293618667= 11*19*6189563*all 15cs
continu.
12  RND(2E9)..=758410764= 2^2*3*19*3326363*all 12cs
13  RND(2E9)..=683539760= 2^4*5*23*269*1381*all 4cs
14  R%(prob-13)..=1008767760= 2^4*3*5*7*11*13*13*17*19*all 3cs
15  R%(prob-13)..=247110827= 17*19*23*29*31*37*all 3cs
16  R%(prob-13)..=259106347= 41*43*47*53*59*all 3cs
17  R%(prob-13)..=1673450759= 61*67*71*73*79*all 3cs
18  R%(prob-13)..=72370439= 83*89*97*101*all 3cs
19  R%(prob-13)..=135745657= 103*107*109*113*all 3cs
20  R%(prob-13)..=316818391= 127*131*137*139*all 3cs
21  R%(prob-13)..=575771909= 149*151*157*163*all 3cs
22  R%(prob-13)..=936039509= 167*173*179*181*all 3cs
23  R%(prob-13)..=1445140189= 191*193*197*199*all 4cs
24  R%(prob-13)..=10579789= 11*19*223*227*all 4cs
25  R%(prob-13)..=12752323= 229*233*239*all 4cs
26  R%(prob-13)..=15546187= 241*251*257*all 4cs
27  R%(prob-13)..=19172437= 263*269*271*all 4cs
28  R%(prob-13)..=22027871= 277*281*283*all 4cs
29  R%(prob-13)..=27974761= 293*307*311*all 4cs
30  R%(prob-13)..=32842151= 313*317*331*all 4cs
31  R%(prob-13)..=40811711= 337*347*349*all 4cs
continu.
32  R%(prob-13)..=46508809= 353*359*367*all 5cs
33  R%(prob-13)..=54143561= 373*379*383*all 5cs
34  R%(prob-13)..=61927633= 389*397*401*all 5cs
35  R%(prob-13)..=74203643= 409*419*433*all 5cs
36  R%(prob-13)..=84986449= 19*23*439*443*all 5cs
37  R%(prob-13)..=94593973= 449*457*461*all 5cs
38  R%(prob-13)..=103569859= 463*467*479*all 5cs
39  R%(prob-13)..=119319383= 487*491*499*all 5cs
40  R%(prob-13)..=133390067= 503*509*521*all 5cs
41  R%(prob-13)..=154769821= 523*541*547*all 5cs
42  R%(prob-13)..=178433279= 557*563*569*all 6cs
43  R%(prob-13)..=193397129= 571*577*587*all 6cs
44  R%(prob-13)..=213479407= 593*599*601*all 6cs
45  R%(prob-13)..=229580147= 607*613*617*all 6cs
46  R%(prob-13)..=250352693= 17*37*619*643*all 6cs
47  R%(prob-13)..=278421569= 647*653*659*all 6cs
48  R%(prob-13)..=301165481= 661*673*677*all 6cs
49  R%(prob-13)..=330839053= 683*691*701*all 7cs
50  R%(prob-13)..=370603517= 709*719*727*all 6cs
51  R%(prob-13)..=402473441= 733*739*743*all 6cs
continu.
52  R%(prob-13)..=432633827= 751*757*761*all 7cs
53  R%(prob-13)..=467821919= 769*773*787*all 7cs
54  R%(prob-13)..=522910903= 797*809*811*all 7cs
55  R%(prob-13)..=558789841= 821*823*827*all 7cs
56  R%(prob-13)..=593287943= 829*839*853*all 7cs
57  R%(prob-13)..=635308669= 857*859*863*all 7cs
58  R%(prob-13)..=682238471= 877*881*883*all 7cs
59  R%(prob-13)..=732907699= 887*907*911*all 8cs
60  R%(prob-13)..=799964687= 919*929*937*all 7cs
61  R%(prob-13)..=849244031= 941*947*953*all 8cs
62  R%(prob-13)..=917360989= 967*971*977*all 8cs
63  R%(prob-13)..=971230541= 983*991*997*all 8cs
64  R%(prob-13)..=1041537223= 1009*1013*1019*all 8cs
65  R%(prob-13)..=1087388483= 1021*1031*1033*all 8cs
66  R%(prob-13)..=1158575393= 1039*1049*1063*all 8cs
67  R%(prob-13)..=1246829219= 29*37*1069*1087*all 9cs
68  R%(prob-13)..=1308131911= 1091*1093*1097*all 8cs
69  R%(prob-13)..=1366344559= 1103*1109*1117*all 9cs
70  R%(prob-13)..=1459314917= 1123*1129*1151*all 8cs
71  R%(prob-13)..=1570239569= 1153*1163*1171*all 9cs
continu.
72  R%(prob-13)..=1672403471= 1181*1187*1193*all 9cs
73  R%(prob-13)..=1772941421= 1201*1213*1217*all 9cs
74  R%(prob-13)..=1850275477= 1223*1229*1231*all 9cs
75  R%(prob-13)..=1945171367= 1237*1249*1259*all 9cs
76  R%(prob-13)..=2079169259= 19*67*1277*1279*all 9cs
77  R%(prob-13)..=2135039017= 1283*1289*1291*all 9cs
78  R%(prob-13)..=1687397= 1297*1301*all 9cs
79  R%(prob-13)..=1703021= 1303*1307*all 10cs
80  R%(prob-13)..=1742399= 1319*1321*all 9cs
81  R%(prob-13)..=1806047= 1327*1361*all 9cs
82  R%(prob-13)..=1876891= 1367*1373*all 9cs
83  R%(prob-13)..=1932019= 1381*1399*all 10cs
84  R%(prob-13)..=2005007= 1409*1423*all 10cs
85  R%(prob-13)..=2039183= 1427*1429*all 10cs
86  R%(prob-13)..=2062087= 1433*1439*all 11cs
87  R%(prob-13)..=2099597= 1447*1451*all 10cs
88  R%(prob-13)..=2119927= 1453*1459*all 10cs
89  R%(prob-13)..=2178527= 13*113*1483*all 3cs
90  R%(prob-13)..=2214143= 1487*1489*all 10cs
91  R%(prob-13)..=2238007= 1493*1499*all 10cs
continu.
92  R%(prob-13)..=2301253= 1511*1523*all 11cs
93  R%(prob-13)..=2362333= 1531*1543*all 10cs
94  R%(prob-13)..=2405597= 1549*1553*all 11cs
95  R%(prob-13)..=2442953= 1559*1567*all 11cs
96  R%(prob-13)..=2480609= 1571*1579*all 11cs
97  R%(prob-13)..=2528051= 1583*1597*all 10cs
98  R%(prob-13)..=2572807= 1601*1607*all 10cs
99  R%(prob-13)..=2595317= 1609*1613*all 10cs
100  R%(prob-13)..=2624399= 1619*1621*all 11cs
101  R%(prob-13)..=2663399= 1627*1637*all 11cs
102  R%(prob-13)..=2755591= 1657*1663*all 11cs
103  R%(prob-13)..=2782223= 1667*1669*all 12cs
104  R%(prob-13)..=2842547= 23*73*1693*all 3cs
105  R%(prob-13)..=2883203= 1697*1699*all 11cs
106  R%(prob-13)..=2941189= 1709*1721*all 11cs
107  R%(prob-13)..=2985959= 1723*1733*all 11cs
108  R%(prob-13)..=3041527= 1741*1747*all 11cs
109  R%(prob-13)..=3083527= 1753*1759*all 12cs
110  R%(prob-13)..=3168391= 1777*1783*all 12cs
111  R%(prob-13)..=3196943= 1787*1789*all 12cs
continu.
112  R%(prob-13)..=3261611= 1801*1811*all 12cs
113  R%(prob-13)..=3337913= 1823*1831*all 12cs
114  R%(prob-13)..=3437267= 1847*1861*all 12cs
115  R%(prob-13)..=3493157= 1867*1871*all 12cs
116  R%(prob-13)..=3515621= 1873*1877*all 12cs
117  R%(prob-13)..=3549431= 1879*1889*all 13cs
118  R%(prob-13)..=3640463= 23*83*1907*all 3cs
119  R%(prob-13)..=3686351= 41*47*1913*all 2cs
120  R%(prob-13)..=3732623= 1931*1933*all 13cs
121  R%(prob-13)..=3802499= 1949*1951*all 12cs
122  R%(prob-13)..=3904567= 1973*1979*all 13cs
123  R%(prob-13)..=3960091= 1987*1993*all 13cs
124  R%(prob-13)..=3992003= 1997*1999*all 13cs
125  R%(prob-13)..=4028033= 2003*2011*all 13cs
126  R%(prob-13)..=4088459= 2017*2027*all 13cs
127  R%(prob-13)..=4137131= 2029*2039*all 13cs
128  R%(prob-13)..=4235339= 2053*2063*all 13cs
129  R%(prob-13)..=4305589= 2069*2081*all 13cs
130  R%(prob-13)..=4347221= 2083*2087*all 14cs
131  R%(prob-13)..=4384811= 2089*2099*all 13cs
continu.
132  R%(prob-13)..=4473221= 29*73*2113*all 3cs
133  R%(prob-13)..=4536899= 2129*2131*all 14cs
134  R%(prob-13)..=4575317= 2137*2141*all 13cs
135  R%(prob-13)..=4613879= 2143*2153*all 14cs
136  R%(prob-13)..=4708819= 2161*2179*all 14cs
137  R%(prob-13)..=4862021= 2203*2207*all 14cs
138  R%(prob-13)..=4915073= 2213*2221*all 14cs
139  R%(prob-13)..=5008643= 2237*2239*all 15cs
140  R%(prob-13)..=5048993= 2243*2251*all 14cs
141  R%(prob-13)..=5143823= 2267*2269*all 14cs
142  R%(prob-13)..=5184713= 2273*2281*all 14cs
143  R%(prob-13)..=5244091= 2287*2293*all 15cs
144  R%(2*prob)..=22953677= 4789*4793*all 27cs
145  R%(2*prob)..=23184221= 4813*4817*all 27cs
146  R%(2*prob)..=23522491= 23*37*131*211*all 3cs
147  R%(2*prob)..=23755867= 4871*4877*all 28cs
148  R%(2*prob)..=24068827= 4903*4909*all 28cs
149  R%(2*prob)..=24354221= 4933*4937*all 29cs
150  R%(2*prob)..=24621419= 4957*4967*all 28cs
151  R%(2*prob)..=24900091= 4987*4993*all 29cs
continu.
152  R%(2*prob)..=25100099= 5009*5011*all 29cs
153  R%(2*prob)..=25462067= 31*163*5039*all 3cs
154  R%(2*prob)..=25735313= 37*137*5077*all 3cs
155  R%(2*prob)..=26009999= 5099*5101*all 29cs
156  R%(2*prob)..=26347493= 5119*5147*all 30cs
157  R%(2*prob)..=26780609= 5171*5179*all 29cs
158  R%(2*prob)..=27227443= 5209*5227*all 30cs
159  R%(2*prob)..=27489013= 29*181*5237*all 4cs
160  R%(2*prob)..=27836167= 5273*5279*all 31cs
161  R%(2*prob)..=28089991= 5297*5303*all 30cs
162  R%(2*prob)..=28515551= 5333*5347*all 30cs
163  R%(2*prob)..=29052091= 5387*5393*all 30cs
164  R%(2*prob)..=29322221= 5413*5417*all 31cs
165  R%(2*prob)..=29582717= 5437*5441*all 31cs
166  R%(2*prob)..=29877107= 13*53*103*421*all 3cs
167  R%(2*prob)..=30161983= 5483*5501*all 31cs
168  R%(2*prob)..=30470399= 5519*5521*all 32cs
169  R%(2*prob)..=30913591= 5557*5563*all 31cs
170  R%(2*prob)..=31203371= 5581*5591*all 32cs
171  R%(2*prob)..=31854727= 5641*5647*all 32cs
continu.
172  R%(2*prob)..=32012963= 5657*5659*all 32cs
173  R%(2*prob)..=32387477= 5689*5693*all 33cs
174  R%(2*prob)..=32649787= 5711*5717*all 32cs
175  R%(2*prob)..=32970563= 5741*5743*all 33cs
176  R%(2*prob)..=33489353= 5783*5791*all 32cs
177  R%(2*prob)..=33837473= 5813*5821*all 33cs
178  R%(2*prob)..=34175707= 5843*5849*all 34cs
179  R%(2*prob)..=34386487= 5861*5867*all 33cs
180  R%(2*prob)..=34751021= 71*83*5897*all 3cs
181  R%(2*prob)..=35105621= 5923*5927*all 34cs
182  R%(2*prob)..=35808247= 5981*5987*all 34cs
183  R%(2*prob)..=36397073= 6029*6037*all 35cs
184  R%(2*prob)..=36723551= 6053*6067*all 34cs
185  R%(2*prob)..=37161167= 17*359*6089*all 4cs
186  R%(2*prob)..=37405447= 29*211*6113*all 4cs
187  R%(2*prob)..=37675019= 6133*6143*all 34cs
188  R%(2*prob)..=38254081= 6173*6197*all 34cs
189  R%(2*prob)..=38613787= 6211*6217*all 36cs
190  R%(2*prob)..=39087479= 6247*6257*all 36cs
191  R%(2*prob)..=39363067= 6271*6277*all 36cs
continu.
192  R%(2*prob)..=39879221= 59*107*6317*all 3cs
193  R%(2*prob)..=40106873= 6329*6337*all 36cs
194  R%(2*prob)..=40449599= 6359*6361*all 36cs
195  R%(2*prob)..=40755431= 6379*6389*all 36cs
196  R%(2*prob)..=41447723= 6427*6449*all 37cs
197  R%(2*prob)..=41951513= 6473*6481*all 37cs
198  R%(2*prob)..=42614783= 61*107*6529*all 3cs
199  R%(2*prob)..=42889397= 6547*6551*all 37cs
200  R%(2*prob)..=43112347= 6563*6569*all 37cs
201  R%(2*prob)..=43428019= 6581*6599*all 37cs
202  R%(2*prob)..=44155961= 6637*6653*all 37cs
203  R%(2*prob)..=44568967= 6673*6679*all 38cs
204  R%(2*prob)..=44916803= 6701*6703*all 38cs
205  R%(2*prob)..=45360221= 6733*6737*all 37cs
206  R%(2*prob)..=45724643= 6761*6763*all 38cs
207  R%(2*prob)..=46049771= 6781*6791*all 38cs
208  R%(2*prob)..=46580621= 6823*6827*all 39cs
209  R%(2*prob)..=46908737= 6841*6857*all 38cs
210  R%(2*prob)..=47293093= 6871*6883*all 39cs
211  R%(2*prob)..=47803387= 6911*6917*all 38cs
continu.
212  R%(2*prob)..=48274703= 6947*6949*all 39cs
213  R%(2*prob)..=48566957= 6967*6971*all 39cs
214  R%(2*prob)..=48916027= 6991*6997*all 40cs
215  R%(2*prob)..=49322513= 7019*7027*all 40cs
216  R%(2*prob)..=49885933= 7057*7069*all 39cs
217  R%(2*prob)..=50623189= 7109*7121*all 40cs
218  R%(2*prob)..=51065267= 11*11*23*59*311*all 3cs
219  R%(2*prob)..=51408899= 67*71*101*107*all 3cs
220  R%(2*prob)..=51696091= 7187*7193*all 40cs
contin.

*  bug?  until false.


problem # =221.   * = 7193  Repeat n1.

R%(2*prob)..=51696091= 7187*7193*all
  Time speed,  sec = 36.11999999
>>221  R%(2*prob)..=51696091= 7187*7193*all 36s.

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

PLEASE ENTER)  numeric expression/no.,
 or  C= 8xCAP letr word(base 100, Z base 27) Ppt= teleph keypad 
n,n1,d (may refer to last factor n/test n1/ or Datum, d)
 e.g. n1+30.  p()=previous prob/ value , P%() prime , R%() primorial.
r.andom test =r,  or
<CR>,  very easy (a)gain,  repeat similar formula.?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. ??  4-2-2003.)

my file > *ram.sumryfact.creditcd1..  Thu,06 Feb 2003.18:36:27
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)
(prob) -- #formula,--  value, --   FACTORS -- ,  (centiseconds).
---   
2  2^48+1  example...=281474976710657= 193*65537*22253377prime 14s.
3  2^51+P%(prob)..=2251799813685261= 3*7*107228562556441? >46201^3 cofactor? 7s.
4  2^51+P%(prob)..=2251799813685265= 5*467*3433*280911223*all 1s.
5  2^51+P%(prob)..=2251799813685267= 3*3*29*2027*4256332261prime 14s.
6  2^51+P%(prob)..=2251799813685271= 2251799813685271? >46201^3 cofactor? 7s.
7  2^51+P%(prob)..=2251799813685277= 31*72638703667267prime 12mn
8  2^51+P%(prob)..=2251799813685279= 3*11*13*707159*7422589prime 1mn
9  2^51+P%(prob)..=2251799813685285= 3*5*3*3* 3mn
10  R%(prob-9)..=1008767760= 2^4*3*5*7*11*13*13*17*19*all 6cs
11  R%(prob-9)..=247110827= 17*19*23*29*31*37*all 5cs
continu.
12  R%(prob-9)..=259106347= 41*43*47*53*59*all 6cs
13  R%(prob-9)..=1673450759= 61*67*71*73*79*all 6cs
14  R%(prob-9)..=72370439= 83*89*97*101*all 6cs
15  R%(prob-9)..=135745657= 103*107*109*113*all 6cs
16  R%(prob-9)..=316818391= 127*131*137*139*all 6cs
17  R%(prob-9)..=575771909= 149*151*157*163*all 6cs
18  R%(prob-9)..=936039509= 167*173*179*181*all 6cs
19  R%(prob-9)..=1445140189= 191*193*197*199*all 6cs
20  R%(prob-9)..=10579789= 11*19*223*227*all 6cs
21  R%(prob-9)..=12752323= 229*233*239*all 6cs
22  R%(prob-9)..=15546187= 241*251*257*all 6cs
23  R%(prob-9)..=19172437= 263*269*271*all 7cs
24  R%(prob-9)..=22027871= 277*281*283*all 6cs
25  R%(prob-9)..=27974761= 293*307*311*all 7cs
26  R%(prob-9)..=32842151= 313*317*331*all 7cs
27  R%(prob-9)..=40811711= 337*347*349*all 7cs
28  R%(400)..=43112347= 6563*6569*all 39cs
29  R%(477)..=60699677= 7789*7793*all 45cs
30  R%(480)..=61387189= 7829*7841*all 45cs
31  R%(490)..=64096027= 53*151*8009*all 6cs
continu.
32  R%(555)..=81812021= 83*109*9043*all 6cs
33  R%(666)..=118026487= 10861*10867*all 61cs
34  R%(888)..=211120891= 73*199*14533*all 6cs
35  R%(999)..=268500947= 11*13*13*97*1489*all 6cs
36  R%(1111)..=331749787= 18211*18217*all 99cs
37  R%(1111)..=331749787= 18211*18217*all 27s.
38  R%(1666)..=755370247= 27481*27487*all 1s.
39  R%(2000)..=1092038107= 173*191*33049*all 7cs
40  R%(2222)..=1348138073= 36713*36721*all 1s.
41  R%(2333)..=1487953451= 173*223*38569*all 6cs
42  R%(2444)..=1628122499= 157*257*40351*all 7cs
43  R%(2666)..=1934240351= 43973*43987*all 2s.
44  R%(2700)..=1982564627= 44519*44533*all 2s.
45  R%(2777)..=2100388891= 45827*45833*all 2s.
46  R%(2888)..=0= 1 (less than 2.X ) 1cs
47  R%(2800)..=2137582747= 83*557*46237*all 8cs
48  R%(2822)..=0= 1 (less than 2.X ) 1cs
contin.

         0 ) 

warning.  negative or decimal (fractional) input may
 result in incomplete factors.*******

*  bug?  until false.


problem # =49.   * = 1  Repeat n1.

R%(2822)..=0= 1 (less than 2.X )
  Time speed,  sec = 91.5700000000000074
>>49  R%(2822)..=0= 1 (less than 2.X ) 1mn

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

PLEASE ENTER)  numeric expression/no.,
 or  C= 8xCAP letr word(base 100, Z base 27) Ppt= teleph keypad 
n,n1,d (may refer to last factor n/test n1/ or Datum, d)
 e.g. n1+30.  p()=previous prob/ value , P%() prime , R%() primorial.
r.andom test =r,  or
<CR>,  very easy (a)gain,  repeat similar formula.?0
enter = close ,  or <ESC> resume.?
e n d. close *spool
