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 2003-10-08, 13:12 #1 alpertron     Aug 2002 Buenos Aires, Argentina 5×269 Posts 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.