View Single Post
Old 2003-10-08, 13:12   #1
alpertron
 
alpertron's Avatar
 
Aug 2002
Buenos Aires, Argentina

53F16 Posts
Default More factors found with a new program

I've just written a program in UBASIC in order to find factors of M(3326400):

10 for A=1 to 100000000
20 J=(2*A+1)*3326400+1
30 if J@3=0 or J@5=0 or J@7=0 or J@11=0 then 220
40 K=modpow(2,3326400,J)
50 if K>1 then 220
60 if modpow(13,J-1,J)<>1 and modpow(17,J-1,J)<>1 then 220
70 Expon=3326400
80 if modpow(2,Expon\2,J)<>1 then 140 else Expon=Expon\2
90 if modpow(2,Expon\2,J)<>1 then 140 else Expon=Expon\2
100 if modpow(2,Expon\2,J)<>1 then 140 else Expon=Expon\2
110 if modpow(2,Expon\2,J)<>1 then 140 else Expon=Expon\2
120 if modpow(2,Expon\2,J)<>1 then 140 else Expon=Expon\2
130 if modpow(2,Expon\2,J)<>1 then 140 else Expon=Expon\2
140 if modpow(2,Expon\3,J)<>1 then 170 else Expon=Expon\3
150 if modpow(2,Expon\3,J)<>1 then 170 else Expon=Expon\3
160 if modpow(2,Expon\3,J)<>1 then 170 else Expon=Expon\3
170 if modpow(2,Expon\5,J)<>1 then 190 else Expon=Expon\5
180 if modpow(2,Expon\5,J)<>1 then 190 else Expon=Expon\5
190 if modpow(2,Expon\7,J)<>1 then 200 else Expon=Expon\7
200 if modpow(2,Expon\11,J)<>1 then 210 else Expon=Expon\11
210 print J;"divides M(";Expon;")"
220 next A


In less than one hour it found the following factors:

56951294401 divides M( 13860 )
88365816001 divides M( 277200 )
129486772801 divides M( 184800 )
245997259201 divides M( 15120 )
276254193601 divides M( 46200 )
642304555201 divides M( 3780 )
934635240001 divides M( 25200 )
1195092360001 divides M( 110880 )
1490170651201 divides M( 110880 )
2529298094401 divides M( 13860 )
3171273336001 divides M( 75600 )
3180287880001 divides M( 831600 )
3445362043201 divides M( 138600 )
4283754552001 divides M( 138600 )
6277838212801 divides M( 27720 )
6523812187201 divides M( 83160 )
6820427275201 divides M( 73920 )
7135197854401 divides M( 207900 )
7321709102401 divides M( 27720 )
7698377332801 divides M( 23760 )
7885387540801 divides M( 7920 )
8179574356801 divides M( 73920 )
9173203300801 divides M( 11088 )
9829076241601 divides M( 55440 )
9880169745601 divides M( 138600 )
10424834481601 divides M( 60480 )
12540657729601 divides M( 5040 )
13473919166401 divides M( 69300 )
14027691585601 divides M( 46200 )
14385073348801 divides M( 69300 )
14798731147201 divides M( 332640 )
14900731876801 divides M( 110880 )
15737381352001 divides M( 1108800 )
16289330904001 divides M( 25200 )
17068593326401 divides M( 415800 )
17085657758401 divides M( 25200 )
20380816209601 divides M( 554400 )
20982648456001 divides M( 158400 )
21567728952001 divides M( 4200 )
23500600200001 divides M( 831600 )
24542508513601 divides M( 7920 )
29599288488001 divides M( 184800 )
32057358379201 divides M( 60480 )
33319846929601 divides M( 83160 )
36861538190401 divides M( 36960 )
36963465739201 divides M( 50400 )
37830804580801 divides M( 277200 )
39750642993601 divides M( 55440 )
40707834552001 divides M( 166320 )
42539816088001 divides M( 138600 )
44406445406401 divides M( 69300 )
45455265979201 divides M( 18480 )
47058258139201 divides M( 1260 )
49527917208001 divides M( 277200 )
54095297256001 divides M( 1663200 )
54788572238401 divides M( 55440 )
59025780475201 divides M( 158400 )
60445820635201 divides M( 221760 )
60712910596801 divides M( 207900 )
61880011300801 divides M( 55440 )
66321014760001 divides M( 55440 )
68302870574401 divides M( 69300 )
68637819096001 divides M( 95040 )
68766238094401 divides M( 55440 )
69686001000001 divides M( 554400 )
75163956436801 divides M( 277200 )
77237920267201 divides M( 207900 )
82523024337601 divides M( 41580 )
83582715585601 divides M( 41580 )
85809986539201 divides M( 221760 )
90686628648001 divides M( 50400 )
91599346238401 divides M( 277200 )
94173800212801 divides M( 332640 )
94386490228801 divides M( 415800 )
98014627972801 divides M( 55440 )
98757652593601 divides M( 554400 )
102422606932801 divides M( 138600 )
104208557745601 divides M( 34650 )
108002909044801 divides M( 665280 )
108068259499201 divides M( 92400 )
112637515636801 divides M( 1663200 )
116337922747201 divides M( 75600 )
117425515838401 divides M( 554400 )
117538207617601 divides M( 43200 )
122700055262401 divides M( 138600 )
125889640430401 divides M( 151200 )
130775343652801 divides M( 138600 )
137826167371201 divides M( 110880 )
139898434737601 divides M( 665280 )
149246856158401 divides M( 332640 )
152858534875201 divides M( 554400 )
156183810552001 divides M( 118800 )
160915202078401 divides M( 3080 )
162810724507201 divides M( 554400 )
177203871028801 divides M( 1663200 )
177909147662401 divides M( 69300 )
178277573073601 divides M( 110880 )
180505349640001 divides M( 415800 )
184952520244801 divides M( 277200 )
188172774820801 divides M( 277200 )
194486987217601 divides M( 16632 )
197172043992001 divides M( 41580 )
200010720571201 divides M( 18900 )
211835972779201 divides M( 554400 )
219380075006401 divides M( 221760 )
226937815473601 divides M( 18480 )
228026685902401 divides M( 138600 )
229761736142401 divides M( 277200 )
232537889707201 divides M( 39600 )
238511079576001 divides M( 554400 )
251133949281601 divides M( 7920 )
256396859611201 divides M( 277200 )
257978695867201 divides M( 18480 )
264015825796801 divides M( 69300 )
265925146132801 divides M( 69300 )
276941431166401 divides M( 332640 )
286333834248001 divides M( 1108800 )
295978025851201 divides M( 20790 )
311020339291201 divides M( 46200 )
314020698868801 divides M( 110880 )
315965132683201 divides M( 831600 )
318420694468801 divides M( 332640 )
330735479659201 divides M( 138600 )
332854150305601 divides M( 7200 )
335632479336001 divides M( 83160 )
345083313960001 divides M( 41580 )
348712356484801 divides M( 166320 )
359673762571201 divides M( 1663200 )
367871336078401 divides M( 59400 )
371240087803201 divides M( 55440 )
376797078504001 divides M( 20790 )
389887946078401 divides M( 277200 )
392592615307201 divides M( 277200 )
400450004539201 divides M( 221760 )
412279574414401 divides M( 1108800 )
413736411211201 divides M( 69300 )
415114924593601 divides M( 415800 )
427635793569601 divides M( 277200 )
430119024350401 divides M( 92400 )
432727620494401 divides M( 50400 )
436919230440001 divides M( 138600 )
447025718462401 divides M( 1980 )
448099267492801 divides M( 184800 )
465550406798401 divides M( 69300 )
468542523556801 divides M( 69300 )
478938381768001 divides M( 46200 )
480789729604801 divides M( 13860 )
483564559262401 divides M( 13860 )
494562622276801 divides M( 831600 )
494681441284801 divides M( 665280 )
510863578948801 divides M( 831600 )
515047731105601 divides M( 831600 )
529264851192001 divides M( 69300 )
530227970395201 divides M( 25200 )
530446089096001 divides M( 55440 )
548837821224001 divides M( 3600 )
559371711729601 divides M( 69300 )
588092248497601 divides M( 207900 )
595389318955201 divides M( 277200 )
611590330612801 divides M( 36960 )
616719679329601 divides M( 27720 )
619119084830401 divides M( 30240 )
624446434180801 divides M( 14850 )
629641552478401 divides M( 18900 )
635122960718401 divides M( 166320 )
646508828750401 divides M( 166320 )
656815645886401 divides M( 554400 )
662910222744001 divides M( 332640 )
664117446484801 divides M( 1663200 )

Notice that more factors can be found in two ways:

1) Changing the range in the first line

2) Changing the number 3326400 by a divisor of it in all lines where this number appear.
alpertron is offline