
(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.  no xxx
factor base 2*3*5*7*11 = 2310. x 480 xx.
bugs xx

my file > *ram.sumryfact.creditcd1..  Sat,08 Feb 2003.18:43:02
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= 99546819636163? >46201^3 cofactor? 6s.
3  2^51..=2251799813685248= 3th powof(17th powof(2*all 3cs
4  d+P%(prob)..=2251799813685267= 3*3*29*2027*4256332261prime 12s.
5  d+P%(prob)..=2251799813685271= 2251799813685271? >46201^3 cofactor? 6s.
6  d+P%(prob)..=2251799813685277= 31*72638703667267prime 11mn
7  d+P%(prob)..=2251799813685279= 3*11*13*707159*7422589prime 1mn
8  d+P%(prob)..=2251799813685285= 3*3*5*3*16679998619891prime 5mn
contin.

my file > *ram.sumryfact.creditcd1..  Sat,08 Feb 2003.19:47:58
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= 99546819636163? >46201^3 cofactor? 6s.
3  3^33..=5559060566555523= Accy?(3th powof(11th powof(3*all 2cs
4  n1+2..=5559060566555525= Accy?(5*5*222362422662221? >46201^3 cofactor? 6s.
5  n1+2..=5559060566555527= Accy?(31*43*4170338009419prime 2mn
6  n1+2..=5559060566555529= Accy?(3*11*139*1211916408667prime 1mn
7  n1+2..=5559060566555531= Accy?(7*25307*31380705319prime 21s.
8  n1+2..=5559060566555533= Accy?(8663*641701554491prime 1mn
9  n1+2..=5559060566555535= Accy?(3*5*13*1213*2729*8611969*all 64cs
10  n1+2..=5559060566555537= Accy?(17*53*157*1669*23546189*all 57cs
11  n1+2..=5559060566555539= Accy?(811*6854575297849prime 3mn
continu.
12  n1+2..=5559060566555541= Accy?(3*3*29*29*734451125189prime 1mn
13  n1+2..=5559060566555543= Accy?(5559060566555543? >46201^3 cofactor? 6s.
14  n1+2..=5559060566555545= Accy?(5*7*23*79*2383*36682117*all 74cs
15  n1+2..=5559060566555547= Accy?(3*227*61547*132631721prime 12s.
16  n1+2..=5559060566555549= Accy?(19*37*37*229*2543*366997*all 23cs
17  n1+2..=5559060566555551= Accy?(11*757*797*837634429*all 1s.
18  n1+2..=5559060566555553= Accy?(3*47*549167*71792299prime 50s.
19  n1+2..=5559060566555555= Accy?(5*1111812113311111? >46201^3 cofactor? 6s.
20  n1+2..=5559060566555557= Accy?(61*103*109*397*20446423*all 35cs
21  n1+2..=5559060566555559= Accy?(3*3*7*7*6073*2075675863*all 3s.
22  n1+2..=5559060566555561= Accy?(13*41*15187*17923*38317*all 3s.
23  n1+2..=5559060566555563= Accy?(101*233*1831*2803*46027*all 48cs
24  n1+2..=5559060566555565= Accy?(3*5*23753*29581*527447*all 4s.
25  n1+2..=5559060566555567= Accy?(6037*471673*1952267prime 45s.

27  P%(480)..=2309= 2309*all 6cs
28  R%(480)..=73153709= 8543*8563*all 50cs
29  R%(900)..=284968157= 16879*16883*all 94cs
30  R%(990)..=350288647= 18713*18719*all 1s.
31  R%(1000)..=359709107= 18959*18973*all 1s.

32  R%(1000)..=359709107= 18959*18973*all 20s.
33  R%(1444)..=812591987= 28499*28513*all 1s.
34  R%(2000)..=1686498389= 41057*41077*all 2s.
35  R%(2222)..=0= 1 (less than 2.X ) 1cs
36  R%(2100)..=1876275847= 43313*43319*all 2s.
37  R%(2150)..=1993533197= 44647*44651*all 2s.
38  R%(2180)..=2053721123= 45317*45319*all 2s.
39  R%(2190)..=2074529173= 45541*45553*all 2s.
40  R%(2200)..=2094435221= 45763*45767*all 2s.
41  R%(2215)..=2126869699= 46103*46133*all 2s.
42  R%(2220)..=0= 1 (less than 2.X ) 1cs
43  p(41)..=2126869699= 46103*46133*all 2s.
44  R%(2218)..=2132777123= 46181*46183*all 2s.
45  R%(2219)..=2133793213= 46187*46199*all 2s.
46  R%(2220)..=0= 1 (less than 2.X ) 1cs
47  p(45)..=2133793213= 46187*46199*all 2s.   ***
48  n*n1..=98579112647387=  1mn
49  n*n1..=98579112647387=  2mn
50  n*n1 bug(teleph kpd)..=66284= 2^2*73*227*all 6cs   ****

my file > *ram.sumryfact.creditcd1..  Sat,08 Feb 2003.20:03:18
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= 99546819636163? >46201^3 cofactor? 6s.
3  R%(2220)..=0= 1 (less than 2.X ) 0cs
4  R%(2215)..=2126869699= 46103*46133*all 2s.
5  n*n1..=98118879823967= 46103*46133*46133*all 8s.
6  n+2..=46135= 5*9227*all 6cs
7  n1+2..=46137= 3*7*13*13*13*all 5cs
8  n1+2..=46139= 29*37*43*all 5cs
9  n1+2..=46141= 46141*all 6cs
10  n1+2..=46143= 3*3*3*1709*all 5cs
11  n1+2..=46145= 5*11*839*all 5cs

12  n1+2..=46147= 46147*all 6cs
13  n1+2..=46149= 3*15383*all 6cs
14  n1+2..=46151= 7*19*347*all 5cs
15  n1+2..=46153= 46153*all 6cs
16  p(9)*p(12)*p(15)..=98272139557231= 46141*46147*46153*all 8s.
17  n+2..=46155= 3*5*17*181*all 5cs
18  n1+2..=46157= 101*457*all 6cs
19  n1+2..=46159= 31*1489*all 5cs
20  n1+2..=46161= 3*3*23*223*all 5cs
21  n1+2..=46163= 13*53*67*all 5cs
22  n1+2..=46165= 5*7*1319*all 5cs
23  n1+2..=46167= 3*11*1399*all 5cs
24  n1+2..=46169= 137*337*all 6cs
25  n1+2..=46171= 46171*all 6cs
26  n1+2..=46173= 3*15391*all 6cs
27  n1+2..=46175= 5*5*1847*all 5cs
28  n1+2..=46177= 61*757*all 5cs
29  n1+2..=46179= 3*3*7*733*all 5cs
30  n1+2..=46181= 46181*all 6cs
31  n1+2..=46183= 46183*all 6cs

32  p(25)*p(30)*p(31)..=98472452546033= 46171*46181*46183*all 8s.
33  n+2..=46185= 3*5*3079*all 5cs
34  n1+2..=46187= 46187*all 6cs
35  n1+2..=46189= 11*13*17*19*all 5cs
36  n1+2..=46191= 3*89*173*all 6cs
37  n1+2..=46193= 7*6599*all 5cs
38  n1+2..=46195= 5*9239*all 6cs
39  n1+2..=46197= 3*3*3*29*59*all 5cs
40  n1+2..=46199= 46199*all 6cs
41  n1+2..=46201= 47*983*all 5cs
42  n1+2..=46203= 3*15401*all 6cs
43  n1+2..=46205= 5*9241*all 5cs
44  n1+2..=46207= 7*7*23*41*all 5cs
45  n1+2..=46209= 3*73*211*all 5cs
46  n1+2..=46211= 11*4201*all 5cs
47  n1+2..=46213= 37*1249*all 5cs
48  n1+2..=46215= 3*3*5*13*79*all 5cs
49  n1+2..=46217= 113*409*all 6cs
50  n1+2..=46219= 46219*all 6cs   too big factor
51  p(34)*p(40)8p(50)..=2133793213= 46187*46199*all 2s.

52  p(34)*p(40)*p(50)..=98621788511647= 46219*2133793213prime 11s.
53  n..=2133793213= 46187*46199*all 2s.
54  p(52) is wrong(telep..=74797664= 2^5*577*4051*all 8cs
contin.


my file > *ram.sumryfact.creditcd1..  Sat,08 Feb 2003.20:45:14
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= 99546819636163? >46201^3 cofactor? 6s.
3  46337^2*46349..=99516752205581= 99516752205581? >46201^3 cofactor? 6s.
4  46337..=46337= 46337*all 6cs
5  n1-2..=46335= 3*5*3089*all 5cs
6  n1-2..=46333= 7*6619*all 5cs
7  n1-2..=46331= 107*433*all 6cs
8  n1-2..=46329= 3*15443*all 6cs
9  n1-2..=46327= 46327*all 6cs
10  n1-2..=46325= 5*5*17*109*all 5cs
11  n1-2..=46323= 3*3*5147*all 6cs
continu.
12  n1-2..=46321= 11*4211*all 6cs
13  n1-2..=46319= 7*13*509*all 5cs
14  n1-2..=46317= 3*15439*all 6cs
15  n1-2..=46315= 5*59*157*all 5cs
16  n1-2..=46313= 29*1597*all 5cs
17  n1-2..=46311= 3*43*359*all 5cs
18  n1-2..=46309= 46309*all 6cs
19  n1*p(9)^2..=99387955731061= 99387955731061? >46201^3 cofactor? 6s.
20  p(9)..=46327= 46327*all 6cs
21  n1-2..=46325= 5*5*17*109*all 5cs
22  n1-2..=46323= 3*3*5147*all 5cs
23  n1-2..=46321= 11*4211*all 5cs
24  n1-2..=46319= 7*13*509*all 5cs
25  n1-2..=46317= 3*15439*all 6cs
26  46201..=46201= 47*983*all 5cs
27  n1-2..=46199= 46199*all 6cs
28  n1-2..=46197= 3*3*3*29*59*all 5cs
29  n1-2..=46195= 5*9239*all 6cs
30  n1-2..=46193= 7*6599*all 5cs
31  n1-2..=46191= 3*89*173*all 5cs
continu.
32  n1-2..=46189= 11*13*17*19*all 5cs
33  n1-2..=46187= 46187*all 6cs
34  n1*p(27)^2..=98579112647387=  35s. ** bug?
35  p(27)..=46199= 46199*all 6cs
36  n1-2..=46197= 3*3*3*29*59*all 5cs
37  n1-2..=46195= 5*9239*all 6cs
38  n1-2..=46193= 7*6599*all 5cs
39  n1-2..=46191= 3*89*173*all 6cs
40  n1-2..=46189= 11*13*17*19*all 5cs
41  n1-2..=46187= 46187*all 6cs
42  n1-2..=46185= 3*5*3079*all 5cs
43  n1-2..=46183= 46183*all 6cs
44  n1^2*p(41)..=98510843088443= 46183*46183*46187*all 8s.


46  p(33)^2*p(27)..=98553507128831=  43s.
47  n1^(1/3)..=46190.9996536321414= Accy?(2*5*31*149*all 5cs



(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.  no xx

my file > *ram.sumryfact.creditcd1..  Sat,08 Feb 2003.21:40:02
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= 99546819636163? >46201^3 cofactor? 6s.
3  46101..=46101= 3*11*11*127*all 5cs
4  n1-2..=46099= 46099*all 6cs
5  n1-2..=46097= 31*1487*all 5cs
6  n1-2..=46095= 3*5*7*439*all 5cs
7  n1-2..=46093= 46093*all 6cs
8  n1^2*p(4)..=97940305754251= 46093*46099*46093*all 8s.
9  n..=46093= 46093*all 6cs
10  n1+2..=46095= 3*5*7*439*all 5cs
11  n1+2..=46097= 31*1487*all 5cs
continu.
12  n1+2..=46099= 46099*all 6cs
13  n*p(9)^2..=97940305754251= 46093*46099*46093*all 8s.
14  n+2..=46095= 3*5*7*439*all 5cs
15  n1+2..=46097= 31*1487*all 5cs
16  n1+2..=46099= 46099*all 6cs
17  n1+2..=46101= 3*11*11*127*all 5cs
18  n1+2..=46103= 46103*all 6cs
19  n1*p(16)^2..=97974305979503= 46099*46099*46103*all 8s. **

20  31,22,27,36,13,08,05,32..lotto

=3122273613080532= 2^2*3*131*104459*19013959prime 15s.

21  2^51..=2251799813685248= 3th powof(17th powof(2*all 2cs
22  d+P%(prob-21)..=2251799813685249= 3*3*307*2857*6529*43691*all 85cs
23  d+P%(prob-21)..=2251799813685261= 3*7*107228562556441? >46201^3 cofactor? 6s.
24  d+P%(prob-21)..=2251799813685265= 5*467*3433*280911223*all 1s.
25  d+P%(prob-21)..=2251799813685267= 3*3*29*2027*4256332261prime 12s.
26  d+P%(prob-21)..=2251799813685271= 2251799813685271? >46201^3 cofactor? 6s.
27  d+P%(prob-21)..=2251799813685277= 31* 26s.
28  d+P%(prob-21)..=2251799813685279= 3*11*13*707159*7422589prime 1mn
29  d+P%(prob-21)..=2251799813685285= 3*3*5*3* 1mn
30  d+P%(prob-21)..=2251799813685289= 7*109*1907*3181*486509*all 52cs
31  d+P%(prob-21)..=2251799813685291= 3*17*41*35983*29928047*all 5s.
continu.
32  d+P%(prob-21)..=2251799813685295= 5*43*1571*5441*1225283*all 97cs
33  d+P%(prob-21)..=2251799813685301= 11*11*59*315422301959prime 50s.
34  R%(prob-33)..=2036934900= 2^2*3*3*5*5*7*7*11*13*17*19*all 5cs
35  R%(prob-33)..=86822723= 13*17*19*23*29*31*all 5cs
36  R%(prob-33)..=162490421= 37*41*43*47*53*all 5cs
37  R%(prob-33)..=1249792339= 59*61*67*71*73*all 5cs
38  R%(prob-33)..=56606581= 79*83*89*97*all 5cs
39  R%(prob-33)..=121330189= 101*103*107*109*all 6cs
40  R%(prob-33)..=257557397= 113*127*131*137*all 6cs
41  R%(prob-33)..=490995677= 139*149*151*157*all 6cs
42  R%(prob-33)..=842952707= 163*167*173*179*all 6cs
43  R%(prob-33)..=1314423991= 181*191*193*197*all 6cs
44  R%(prob-33)..=2125525169= 199*211*223*227*all 6cs
45  RND(606)*2*3*5*7*11*..=771756766020413= 1511*2273*224706971*all 1s.
46  RND(606)*2*3*5*7*11*..=1996178558264119= 43*137*9749*34757641*all 1s.
47  RND(606)*2*3*5*7*11*..=1884867486241909= 13*144989806633993? >46201^3 cofactor? 6s.
48  RND(606)*2*3*5*7*11*..=3754893496213969= 3754893496213969? >46201^3 cofactor? 6s.
49  RND(606)*2*3*5*7*11*..=140994024561587= 83*585619*2900731prime 53s.
50  RND(2^15.5)*RND(2^31..=4896722400465= 3*5*7*17*127*21600487*all 31cs
51  RND(2^15.5)*RND(2^31..=50353238505280= 2^2*5*2^2*2^2*23*83*5939*13879*all 39cs
continu.
52  RND(2^15.5)*RND(2^31..=1362966488652= 2^2*3*347*327321443*all 1s.
53  RND(2^15.5)*RND(2^31..=3683516063134= 2*53*571*60858409*all 54cs
54  RND(2^15.5)*RND(2^31..=2534417010520= 2^2*5*17*2*67*73*863*883*all 13cs
55  RND(2^15.5)*RND(2^31..=14454913495218= 2*3*7*991*347290219*all 1s.
56  RND(2^15.5)*RND(2^31..=36723706856278= 2*13*29*271*661*271897*all 14cs
57  RND(2^15.5)*RND(2^31..=717225278086= 2*601*596693243*all 1s.
58  RND(2^15.5)*RND(2^31..=42404367684900= 2^2*3*5*5*13*17*4397*145459*all 29cs
59  RND(2^15.5)*RND(2^31..=9084282713583= 3*7*7*11*41*379*361541*all 11cs
60  RND(2^15.5)*RND(2^31..=19823621944300= 2^2*5*5*1741*113863423*all 86cs
61  RND(2^15.5)*RND(2^31..=16103703290688= 2^2*3*3*13*2^4*13*29*5704513*all 20cs
62  RND(2^15.5)*RND(2^31..=20376330625476= 2^2*3*3*7*15233*5308111*all 2s.
63  RND(2^15.5)*RND(2^31..=23592220791288= 2^2*3*2*23*29*23*1123*57059*all 13cs
64  RND(2^15.5)*RND(2^31..=68083044630219= 3*3*307*1129*1481*14737*all 30cs
65  RND(2^15.5)*RND(2^31..=57194594941394= 2*83*463*744159293*all 1s.
66  RND(2^15.5)*RND(2^31..=27122549496858= 2*3*3*3*9613*52248979*all 1s.
67  RND(2^15.5)*RND(2^31..=27821488867120= 2^2*5*13*2^2*13*971*2119261*all 15cs
68  RND(2^15.5)*RND(2^31..=7363804976544= 2^2*3*19*2^3*29*2707*51427*all 22cs
69  RND(2^15.5)*RND(2^31..=47821163688970= 2*5*7*43*727*2837*7703*all 32cs
70  RND(2^15.5)*RND(2^31..=26781062500517= 13*103*131*1091*139943*all 15cs
71  RND(2^15.5)*RND(2^31..=492708541759= 7*89*109*127*57131*all 9cs
continu.
72  RND(2^15.5)*RND(2^31..=45495267414515= 5*9187*990427069*all 3s.
73  RND(2^15.5)*RND(2^31..=67589722883088= 2^2*3*3*7*19*2^2*3*3*281*653*2137*all 11cs
74  RND(2^15.5)*RND(2^31..=29355152990475= 3*5*5*13*233*129218237*all 67cs
75  RND(2^15.5)*RND(2^31..=4454665515630= 2*3*3*5*11*19*3*41*41*151*311*all 7cs
76  RND(2^15.5)*RND(2^31..=31514727879936= 2^2*3*3*7*2^2*2^4*1954038187*all 2s.
77  RND(2^15.5)*RND(2^31..=39062933771274= 2*3*3*7*7*3*23*109*5888717*all 20cs
78  n..=5888717= 5888717*all 17cs

79  RND(606)*2*3*5*7*11*..=3569375042843821= 967*186763*19764001prime 22s.
80  RND(606)*2*3*5*7*11*..=2626941299722913= 43*181*337522973111prime 52s.
81  n..=337522973111= 337522973111prime 52s.
82  loto 8-2-2003(teleph..=5686= 2*2843*all 5cs
83  loto 8-2-2003(teleph..=5686= 2*2843*all 1mn


84  46201..=46201= 47*983*all 5cs
85  n1-2..=46199= 46199*all 6cs
86  n1-2..=46197= 3*3*3*29*59*all 5cs
87  n1-2..=46195= 5*9239*all 6cs
88  n1-2..=46193= 7*6599*all 5cs
89  n1-2..=46191= 3*89*173*all 6cs
90  n1-2..=46189= 11*13*17*19*all 5cs
91  n1-2..=46187= 46187*all 6cs
continu.
92  n1^2*p(85)..=98553507128831=  1mn   **bug.
93  n1^2*p(85)..=98553507128831=  2mn

95  46187..=46187= 46187*all 6cs
96  n1-2..=46185= 3*5*3079*all 5cs
97  n1-2..=46183= 46183*all 6cs

99  n..=46183= 46183*all 6cs
100  n^2*p(95)..=98510843088443= 46183*46183*46187*all 8s.

102  46201..=46201= 47*983*all 6cs
103  n1-2..=46199= 46199*all 6cs
104  n1*(2^31-1)..=99211597007753=  36s.   bug.
105  2^31-1..=2147483647= 2147483647*all 2s.
106  2^33-4..=8589934588= 2^2*2147483647*all 2s.
107  2^15+1..=32769= 3*3*11*331*all 5cs
108  n1+2..=32771= 32771*all 6cs
109  n1*(2^31-1)..=70375186595837= 32771*2147483647*all 6s.
110  n^15.5..=4.41481910631036379E144=  34s.
111  INT(2^15.5)..=46340= 2^2*5*7*331*all 5cs
continu.
112  n1-1..=46339= 149*311*all 6cs
113  n1-2..=46337= 46337*all 6cs               **
114  n1-2..=46335= 3*5*3089*all 5cs
115  n1-2..=46333= 7*6619*all 6cs
116  n1-2..=46331= 107*433*all 6cs
117  n1-2..=46329= 3*15443*all 6cs
118  n1-2..=46327= 46327*all 6cs
contin.
