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Old 2003-10-08, 19:48   #7
alpertron
 
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Aug 2002
Buenos Aires, Argentina

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I changed the program so all factors of M (n) that have factors less than 100 are discarded, so the list given in the first two messages of this thread was reduced a lot (and the program runs much faster):

88365816001 (433 x 3697 x 55201) divides M( 277200 )
4283754552001 (181 x 281 x 353 x 397 x 601) divides M( 138600 )
9829076241601 (prime) divides M( 55440 )
68302870574401 (199 x 397 x 8317 x 103951) divides M( 69300 )
94173800212801 (541 x 757 x 12097 x 19009) divides M( 332640 )
94386490228801 (127 x 199 x 617 x 2161 x 2801) divides M( 415800 )
116337922747201 (1201 x 1601 x 2801 x 21601) divides M( 75600 )
180505349640001 (prime) divides M( 415800 )
295978025851201 (463 x 4159 x 9241 x 16633) divides M( 20790 )
335632479336001 (113 x 241 x 617 x 1321 x 15121) divides M( 83160 )
760954505572801 (211 x 631 x 661 x 1801 x 4801) divides M( 277200 )
804209660654401 (1321 x 7393 x 8317 x 9901) divides M( 138600 )
872093734142401 (113 x 241 x 401 x 3697 x 21601) divides M( 415800 )

So the entire list given at the beginning has only two primes and they are already known.

It is obvious that this program cannot find a new factor, but for the record this is the source code:

10 for A=1 to 160000000
20 J=(2*A+1)*3326400+1
30 if J@13=0 or J@17=0 or J@19=0 or J@23=0 then 260
40 if J@29=0 or J@31=0 or J@37=0 or J@41=0 then 260
50 if J@43=0 or J@47=0 or J@53=0 or J@59=0 then 260
60 if J@61=0 or J@67=0 or J@71=0 or J@73=0 then 260
70 if J@79=0 or J@83=0 or J@89=0 or J@97=0 then 260
80 K=modpow(2,3326400,J)
90 if K>1 then 260
100 if modpow(13,J-1,J)<>1 or modpow(17,J-1,J)<>1 then 260
110 Expon=3326400
120 if modpow(2,Expon\2,J)<>1 then 180 else Expon=Expon\2
130 if modpow(2,Expon\2,J)<>1 then 180 else Expon=Expon\2
140 if modpow(2,Expon\2,J)<>1 then 180 else Expon=Expon\2
150 if modpow(2,Expon\2,J)<>1 then 180 else Expon=Expon\2
160 if modpow(2,Expon\2,J)<>1 then 180 else Expon=Expon\2
170 if modpow(2,Expon\2,J)<>1 then 180 else Expon=Expon\2
180 if modpow(2,Expon\3,J)<>1 then 210 else Expon=Expon\3
190 if modpow(2,Expon\3,J)<>1 then 210 else Expon=Expon\3
200 if modpow(2,Expon\3,J)<>1 then 210 else Expon=Expon\3
210 if modpow(2,Expon\5,J)<>1 then 230 else Expon=Expon\5
220 if modpow(2,Expon\5,J)<>1 then 230 else Expon=Expon\5
230 if modpow(2,Expon\7,J)<>1 then 240 else Expon=Expon\7
240 if modpow(2,Expon\11,J)<>1 then 250 else Expon=Expon\11
250 print J;"divides M(";Expon;")"
260 next A

The factors inside parenthesis were inserted manually using my applet.
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