>>  D.Pgms.maths.BigNum.sumsqxcub
06.02.03  21:47
========


(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 2003.21:10:01
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  46339..=46339= 149*311*all 6cs
3  n1^3..=99503870056219= 3th powof(149*311*all 6cs
4  n1+2..=99503870056221= 3* 32s. ?? interrupt


5  n1+2..=99503870056223= 733*6971*19473361*all 1s.
6  n1+2..=99503870056225= 5*5*17299*230080051*all 3s.
7  n1+2..=99503870056227= 3*7*13*19*3*3*73*163*271*661*all 9cs
8  n1+2..=99503870056229= 17* 50s.
9  n1+2..=99503870056231= 6011*16553630021prime 20s.
10  46201..=46201= 47*983*all 5cs
11  n1+2..=46203= 3*15401*all 5cs
continu.
12  n1+2..=46205= 5*9241*all 5cs
13  n1+2..=46207= 7*7*23*41*all 5cs
14  n1+2..=46209= 3*73*211*all 5cs
15  n1+2..=46211= 11*4201*all 5cs
16  n1+2..=46213= 37*1249*all 5cs
17  n1+2..=46215= 3*3*5*13*79*all 5cs
18  n1+2..=46217= 113*409*all 5cs
19  n1+2..=46219= 46219*all 6cs

22  n1+2..=46221= 3*7*31*71*all 5cs
23  n1+2..=46223= 17*2719*all 5cs
24  n1+2..=46225= squareof(5*43*all 5cs
25  n1+2..=46227= 3*19*811*all 5cs
26  n1+2..=46229= 46229*all 6cs

28  p(26)*46219^2..=98754203081069= 46219*46229*46219*all 10s.
29  n..=46219= 46219*all 6cs
30  n1+2..=46221= 3*7*31*71*all 5cs
31  n1+2..=46223= 17*2719*all 5cs
continu.
32  n1+2..=46225= squareof(5*43*all 5cs
33  n1+2..=46227= 3*19*811*all 5cs
34  n1+2..=46229= 46229*all 6cs

37  n1+2..=46231= 83*557*all 5cs
38  n1+2..=46233= 3*3*11*467*all 5cs
39  n1+2..=46235= 5*7*1321*all 5cs
40  n1+2..=46237= 46237*all 6cs

42  p(40)^2*46229..=98831137752701= 46229*46237*46237*all 10s.
43  n+2..=46239= 3*15413*all 5cs
44  n1+2..=46241= 13*3557*all 5cs
45  n1+2..=46243= 131*353*all 5cs
46  n1+2..=46245= 3*5*3083*all 5cs
47  n1+2..=46247= 103*449*all 5cs
48  n1+2..=46249= 7*6607*all 5cs
49  n1+2..=46251= 3*3*3*3*571*all 5cs
50  n1+2..=46253= 23*2011*all 5cs
51  n1+2..=46255= 5*11*29*29*all 5cs
continu.
52  n1+2..=46257= 3*17*907*all 5cs
53  n1+2..=46259= 167*277*all 6cs
54  n1+2..=46261= 46261*all 6cs
55  n1+2..=46261= 46261*all 31s.
56  p(54)^2*p(40)..=98950884554677= 46237*46261*46261*all 10s.
57  n..=46261= 46261*all 6cs
58  n1+2..=46263= 3*7*2203*all 5cs
59  n1+2..=46265= 5*19*487*all 5cs
60  n1+2..=46267= 13*3559*all 6cs
61  n1+2..=46269= 3*3*53*97*all 6cs
62  n1+2..=46271= 46271*all 6cs
63  n1+2..=46273= 46273*all 6cs
64  p(63)^2*p(62)..=99075026967359= 46271*46273*46273*all 10s.
65  Q%(1)..=128731= 23*29*193*all 5cs
66  n1-2..=128729= 109*1181*all 6cs
67  n1-2..=128727= 3*3*14303*all 6cs
68  n1-2..=128725= 5*5*19*271*all 5cs
69  n1-2..=128723= 7*7*37*71*all 6cs
70  n1-2..=128721= 3*107*401*all 6cs
71  n1-2..=128719= 97*1327*all 6cs
continu.
72  n1-2..=128717= 128717*all 7cs
73  n1-2..=128715= 3*5*8581*all 6cs
74  n1-2..=128713= 13*9901*all 6cs
75  n1-2..=128711= 11*11701*all 6cs
76  n1-2..=128709= 3*3*3*3*7*227*all 5cs
77  n1-2..=128707= 17*67*113*all 6cs
78  n1-2..=128705= 5*25741*all 6cs
79  n1-2..=128703= 3*42901*all 6cs
80  n1-2..=128701= 179*719*all 6cs
81  n1-2..=128699= 41*43*73*all 6cs
82  n1-2..=128697= 3*42899*all 6cs
83  n1-2..=128695= 5*7*3677*all 6cs
84  n1-2..=128693= 128693*all 7cs

85  p(84)^2*p(72)..=2131796569746533= 2131796569746533? >46201^3 cofactor? 8s.
86  p(84)^2*p(72)..=2131796569746533= 2131796569746533? >46201^3 cofactor? 3mn

87  2^16..=65536= squareof(squareof(squareof(squareof(2*all 2cs
88  n1+1..=65537= 65537*all 6cs
89  n1+2..=65539= 65539*all 6cs
90  n1+2..=65541= 3*7*3121*all 6cs
91  n1+2..=65543= 65543*all 7cs
continu.
92  n1+2..=65543= 65543*all 24s.

93  p(89)^2*p(91)..=281530814627903= 281530814627903? >46201^3 cofactor? 8s.
94  2^15.9..=61147.250133356225= Accy?(47*1301*all 5cs

95  INTn1..=61147= 47*1301*all 5cs
96  n1+2..=61149= 3*11*17*109*all 5cs
97  n1+2..=61151= 61151*all 6cs
98  n1+2..=61153= 61153*all 6cs
99  p(97)^2*p(98)..=228678267915553= 228678267915553? >46201^3 cofactor? 8s.
100  2^15.6..=49667.000451412714= Accy?(49667*all 6cs
101  INT(n1+2)..=49669= 49669*all 6cs
102  INT(n1+2)..=49671= 3*3*5519*all 6cs
103  INT(n1+2)..=49673= 13*3821*all 6cs
104  INT(n1+2)..=49675= 5*5*1987*all 5cs
105  INT(n1+2)..=49677= 3*29*571*all 5cs
106  INT(n1+2)..=49679= 7*47*151*all 6cs
107  INT(n1+2)..=49681= 49681*all 6cs
108  INT(n1+2)..=49683= 3*16561*all 6cs
109  INT(n1+2)..=49685= 5*19*523*all 5cs
110  INT(n1+2)..=49687= 11*4517*all 6cs
111  INT(n1+2)..=49689= 3*3*5521*all 6cs
continu.
112  INT(n1+2)..=49691= 17*37*79*all 5cs
113  INT(n1+2)..=49693= 7*31*229*all 6cs
114  INT(n1+2)..=49695= 3*5*3313*all 6cs
115  INT(n1+2)..=49697= 49697*all 6cs

116  p(107)^2*p(115)..=122662222916417= 122662222916417? >46201^3 cofactor? 8s.

118  46273..=46273= 46273*all 6cs
119  n1+2..=46275= 3*5*5*617*all 5cs
120  n1+2..=46277= 7*11*601*all 5cs
121  n1+2..=46279= 46279*all 6cs
122  n1+2..=46281= 3*15427*all 6cs
123  n1+2..=46283= 31*1493*all 5cs
124  n1+2..=46285= 5*9257*all 6cs
125  n1+2..=46287= 3*3*37*139*all 6cs
126  n1+2..=46289= 41*1129*all 6cs
127  n1+2..=46291= 7*17*389*all 5cs
128  n1+2..=46293= 3*13*1187*all 5cs
129  n1+2..=46295= 5*47*197*all 6cs
130  n1+2..=46297= 67*691*all 6cs
131  n1+2..=46299= 3*11*23*61*all 5cs
continu.
132  n1+2..=46301= 46301*all 6cs
133  n1+2..=46303= 19*2437*all 5cs
134  n1+2..=46305= 3*3*3*5*7*7*7*all 5cs
135  n1+2..=46307= 46307*all 6cs
136  n1+2..=46309= 46309*all 6cs
137  n1+2..=46311= 3*43*359*all 6cs
138  n1+2..=46313= 29*1597*all 5cs
139  n1+2..=46315= 5*59*157*all 5cs
140  n1+2..=46317= 3*15439*all 6cs
141  n1+2..=46319= 7*13*509*all 5cs
142  n1+2..=46321= 11*4211*all 6cs
143  n1+2..=46323= 3*3*5147*all 6cs
144  n1+2..=46325= 5*5*17*109*all 5cs
145  n1+2..=46327= 46327*all 6cs
146  n1+2..=46329= 3*15443*all 6cs
147  n1+2..=46331= 107*433*all 6cs
148  n1+2..=46333= 7*6619*all 6cs
149  n1+2..=46335= 3*5*3089*all 6cs
150  n1+2..=46337= 46337*all 6cs
151  n1+2..=46339= 149*311*all 6cs
continu.
152  n1+2..=46341= 3*3*19*271*all 5cs
153  n1+2..=46343= 11*11*383*all 5cs
154  n1+2..=46345= 5*13*23*31*all 5cs
155  n1+2..=46347= 3*7*2207*all 5cs
156  n1+2..=46349= 46349*all 6cs
157  p(150)^2*p(156)..=99516752205581= 46337*46337*46349*all 8s.
158  n+2..=46351= 46351*all 6cs
159  n1+2..=46353= 3*15451*all 6cs
160  n1+2..=46355= 5*73*127*all 6cs
161  n1+2..=46357= 151*307*all 6cs
162  n1+2..=46359= 3*3*3*17*101*all 5cs
163  n1+2..=46361= 7*37*179*all 5cs
164  n1+2..=46363= 71*653*all 6cs
165  n1+2..=46365= 3*5*11*281*all 6cs
166  n1+2..=46367= 199*233*all 6cs
167  n1+2..=46369= 89*521*all 6cs
168  n1+2..=46371= 3*13*29*41*all 6cs
169  n1+2..=46373= 79*587*all 6cs
170  n1+2..=46375= 5*5*5*7*53*all 5cs
171  n1+2..=46377= 3*3*5153*all 6cs
continu.
172  n1+2..=46379= 19*2441*all 5cs
173  n1+2..=46381= 46381*all 6cs

...
201  n1+2..=46437= 3*23*673*all 5cs
202  n1+2..=46439= 46439*all 6cs
203  n1+2..=46441= 46441*all 6cs
204  p(202)^2*p(203)..=100153765263961= 100153765263961? >46201^3 cofactor? 8s.
205  p(158)^2*p(173)..=99645645437581= 99645645437581? >46201^3 cofactor? 8s.
206  p(156)^2*p(158)..=99572599506151= 99572599506151? >46201^3 cofactor? 8s.

207  p(150)^2*p(158)..=99521046440719= 46337*46337*46351*all 8s.

209  p(150)*p(156)^2..=99542524288937= 46337*46349*46349prime 13s.

211  p(150)*p(156)*p(158)..=99546819636163*** good.
**************= 46337*46349*46351prime 13s.


p(150)*p(156)*p(158)..=99546819636163= 46337*46349*46351prime
  Time speed,  sec = 361.889999999999986
>>212  p(150)*p(156)*p(158)..=99546819636163= 46337*46349*46351prime 6mn

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 2003.20:03:01
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  109^2*110^3+1..=15813611001= 3*3*2963*593003*all 23cs
3  (prob+100)^2*(prob+101)^3+1..

=11933682177= 3*257*15478187*all 31cs
4  (prob+100)^2*(prob+1..=12520872001= 11*11*113*915737*all 12cs
5  (prob+100)^2*(prob+1..=13130951401= 97*593*228281*all 11cs
6  (prob+100)^2*(prob+1..=13764583149= 3*283*811*19991*all 16cs
7  (prob+100)^2*(prob+1..=14422442689= 19*759075931*all 1s.
8  (prob+100)^2*(prob+1..=15105218257= 1913*7896089*all 53cs
9  (prob+100)^2*(prob+1..=15813611001= 3*3*2963*593003*all 23cs
10  (prob+100)^2*(prob+1..=16548335101= 5449*3036949*all 1s.
11  (prob+100)^2*(prob+1..=17310117889= 109*158808421*all 74cs
continu.
12  (prob+100)^2*(prob+1..=18099699969= 3*13*53*8756507*all 22cs
13  (prob+100)^2*(prob+1..=18917835337= 43*197*2233247*all 15cs
14  (prob+100)^2*(prob+1..=19765291501= 15391*1284211*all 3s.
15  (prob+100)^2*(prob+1..=20642849601= 3*11*983*636359*all 12cs
16  (prob+100)^2*(prob+1..=21551304529= 1013*21274733*all 45cs
17  (prob+100)^2*(prob+1..=22491465049= 1291*641*27179*all 29cs
18  (prob+100)^2*(prob+1..=23464153917= 3*3*41*63588493*all 50cs
19  (prob+100)^2*(prob+1..=24470208001= 23*37*28754651*all 35cs
20  (prob+100)^2*(prob+1..=25510478401= 29*229*3841361*all 17cs
21  (prob+100)^2*(prob+1..=26585830569= 3*93263*95021prime 17s.
22  (prob+100)^2*(prob+1..=27697144429= 5501*5034929*all 1s.
23  (prob+100)^2*(prob+1..=28845314497= 1489*19372273*all 52cs
24  (prob+100)^2*(prob+1..=30031250001= 3*1163*8607409*all 39cs
25  (prob+100)^2*(prob+1..=31255875001= 13*23*137*763027*all 12cs
26  (prob+100)^2*(prob+1..=32520128509= 11*19*71*103*21277*all 8cs
27  (prob+100)^2*(prob+1..=33824964609= 3*3*3*1252776467*all 1s.
28  (prob+100)^2*(prob+1..=35171352577= 35171352577prime 26s.

30  (prob+100)^2*(prob+101)^3


..=37992737900= 2^2*5*13*13*5*131*131*131*all 7cs
31  (prob+100)^2*(prob+1..=39469750848= 2^5*3*11*2*3*3*11*11*131*131*all 8cs
continu.
32  (prob+100)^2*(prob+1..=40992347088= 2^4*3*7*11*19*3*7*7*11*19*19*all 7cs
33  (prob+100)^2*(prob+1..=42561573656= 2^3*7*19*7*19*67*67*67*all 8cs
34  (prob+100)^2*(prob+1..=44178493500= 2^2*3*5*3*3*3*3*3*3*3*3*5*5*67*67*all 8cs
35  (prob+100)^2*(prob+1..=45844185600= 2^5*3*5*17*2^4*3*3*3*3*3*5*17*17*all 7cs
36  (prob+100)^2*(prob+1..=47559745088= 2^5*17*2*17*137*137*137*all 8cs
37  (prob+100)^2*(prob+1..=49326283368= 2^3*3*3*3*23*23*23*137*137*all 7cs
38  (prob+100)^2*(prob+1..=51144928236= 2^2*3*3*23*23*139*139*139*all 8cs
39  (prob+100)^2*(prob+1..=53016824000= 2^5*5*7*2*5*5*7*7*139*139*all 7cs
40  (prob+100)^2*(prob+1..=54943131600= 2^4*3*5*7*3*3*5*7*47*47*47*all 8cs
41  (prob+100)^2*(prob+1..=56925028728= 2^3*3*3*47*47*71*71*71*all 8cs
42  (prob+100)^2*(prob+1..=58963709948= 2^2*11*13*13*11*11*13*71*71*all 8cs
43  (prob+100)^2*(prob+1..=61060386816= squareof(2^6*3*3*3*11*13*all 6cs
44  (prob+100)^2*(prob+1..=63216288000= 2^5*3*5*2^3*3*3*3*5*5*29*29*29*all 7cs
45  (prob+100)^2*(prob+1..=65432659400= 2^3*5*5*29*29*73*73*73*all 7cs
46  (prob+100)^2*(prob+1..=67710764268= 2^2*3*7*3*3*7*7*7*7*7*73*73*all 7cs
47  (prob+100)^2*(prob+1..=70051883328= 2^5*3*7*2*3*7*7*7*37*37*37*all 7cs
48  (prob+100)^2*(prob+1..=72457314896= 2^4*37*37*149*149*149*all 9cs
49  (prob+100)^2*(prob+1..=74928375000= 2^3*3*5*3*3*5*5*5*5*5*149*149*all 7cs
50  (prob+100)^2*(prob+1..=77466397500= 2^2*3*5*3*5*5*5*151*151*151*all 7cs
51  (prob+100)^2*(prob+1..=80072734208= 2^5*19*2^4*19*19*151*151*all 8cs
continu.
52  (prob+100)^2*(prob+1..=82748755008= 2^5*3*17*19*2*3*3*3*3*3*17*17*19*all 7cs
53  (prob+100)^2*(prob+1..=85495847976= 2^3*3*7*11*17*3*3*3*7*7*11*11*17*all 7cs
54  (prob+100)^2*(prob+1..=88315419500= 2^2*5*7*11*5*5*7*11*31*31*31*all 8cs
55  (prob+100)^2*(prob+1..=91208894400= 2^5*3*5*13*13*2*3*3*5*13*31*31*all 6cs
56  (prob+100)^2*(prob+1..=94177716048= 2^4*3*13*13*3*157*157*157*all 7cs
57  (prob+100)^2*(prob+1..=97223346488= 2^3*79*79*79*157*157*all 8cs
58  (prob+100)^2*(prob+1..=100347266556= 2^2*3*3*3*53*53*53*79*79*all 8cs
59  (prob+100)^2*(prob+1..=103550976000= 2^5*3*5*2^10*3*5*5*53*53*all 7cs
60  (prob+100)^2*(prob+1..=106835993600= 2^5*5*7*2^5*5*7*7*23*23*23*all 7cs
61  (prob+100)^2*(prob+1..=110203857288= 2^3*3*7*3*3*3*3*3*3*3*3*3*3*3*7*23*23*all 8cs
62  (prob+100)^2*(prob+1..=113656124268= 2^2*3*3*3*3*3*3*3*3*163*163*163*all 9cs
63  (prob+100)^2*(prob+1..=117194371136= 2^5*2*41*41*41*163*163*all 8cs
64  (prob+100)^2*(prob+1..=120820194000= 2^4*3*5*11*3*3*5*5*11*11*41*41*all 8cs
65  (prob+100)^2*(prob+1..=124535208600= 2^3*3*5*11*3*5*11*83*83*83*all 8cs
66  (prob+100)^2*(prob+1..=128341050428= 2^2*83*83*167*167*167*all 10cs
67  (prob+100)^2*(prob+1..=132239374848= 2^5*3*7*2^4*3*3*7*7*167*167*all 8cs
68  (prob+100)^2*(prob+1..=136231857216= squareof(2^3*3*7*13*13*13*all 5cs

70  2^51+P%(prob-69)..=2251799813685249= 3*3*307*2857*6529*43691*all 95cs
71  2^51+P%(prob-69)..=2251799813685259= 2251799813685259? >46201^3 cofactor? 8s.
continu.
72  2^51+P%(prob-69)..=2251799813685261= 3*7*107228562556441? >46201^3 cofactor? 8s.
73  2^51+P%(prob-69)..=2251799813685265= 5*467*3433*280911223*all 1s.
74  2^51+P%(prob-69)..=2251799813685267= 3*3*29*2027*4256332261prime 15s.
75  2^51+P%(prob-69)..=2251799813685271= 2251799813685271? >46201^3 cofactor? 8s.
76  2^51+P%(prob-69)..=2251799813685277= 31*72638703667267prime 12mn
77  2^51+P%(prob-69)..=2251799813685279= 3*11*13* 40s.

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
