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-   -   Operation: Billion Digits (https://www.mersenneforum.org/showthread.php?t=2235)

 clowns789 2004-03-15 00:08

Operation: Billion Digits

I'd like for some people to join me in the quest for both a billion-digit prime and \$250,000. From the benchmarks and Prime95, I found the lowest prime (just the exponent obviously) in this category was M3321928097. I'd like to have someone start off by advanced factoring it. You should probably do 50 bits. Please reply if you want to take this exponent. But be sure to specify the amount of bits you are factoring with. You me also post comments if necessary.

 dsouza123 2004-03-15 02:24

2^3321928097 - 1
6643856195 is the starting factor
.......................................!
6158854691839 is a FACTOR of
2^3321928097 - 1

k*2*p + 1
927*2*3321928097 + 1

 Uncwilly 2004-03-15 04:09

Next canidates: 3321928109, 3321928121, 3321928171

 wblipp 2004-03-15 05:02

[QUOTE=Uncwilly]Next canidates: 3321928109, 3321928121, 3321928171[/QUOTE]

408676883681617 divides 2^3321928109

408676883681617 = 61512*2*p+1

 wblipp 2004-03-15 05:05

[QUOTE=Uncwilly]Next canidates: 3321928109, 3321928121, 3321928171[/QUOTE]

684317192927 divides 2^3321928121-1

684317192927 = 103*2*p+1

 ET_ 2004-03-15 11:34

[QUOTE=wblipp]684317192927 divides 2^3321928121-1

684317192927 = 103*2*p+1[/QUOTE]

3,321,928,171 no factor up to 60.033 bits, k=179,309,108

Luigi

 ET_ 2004-03-15 13:57

[QUOTE=ET_]3,321,928,171 no factor up to 60.033 bits, k=179,309,108

Luigi[/QUOTE]

Factorization of 3,321,928,097 - 3,321,928,109 and 3,321,928,121 taken up to 60 bits.
Here is the results file

[CODE]
M3321928097 has a factor: 6158854691839
M3321928097 has a factor: 41457662650561
M3321928109 has a factor: 408676883681617
M3321928121 has a factor: 684317192927
M3321928121 has a factor: 502959849088127

[/CODE]

All factors will be sent to Will Edgington if no other did it.

Luigi

 jinydu 2004-03-16 12:47

Just wondering. Does anyone know how many P90 CPU Hours are needed to LL test an exponent, n (as a function of n)?

 Prime95 2004-03-16 13:59

Doubling the exponent results in at least four times the execution time.

 Nuri 2004-03-16 19:18

So, a billion exponent would take a time that is equivalent to ~25,000 2^20,996,011-1 tests??? Wow. :surrender

 nfortino 2004-03-16 19:52

[QUOTE=Nuri]So, a billion exponent would take a time that is equivalent to ~25,000 2^20,996,011-1 tests??? Wow. :surrender[/QUOTE]

The LL test is actually O(N[sup]2[/sup]logN), since it is an O(NlogN) FFT multiply performed N times. Accounting for the extra term, it would take ~32,000 times the time it took to test M40. For numbers of this size, it makes much more sense to use numbers which can be tested using Proth's theorem, allowing many numbers with almost exactly 1 billion digits to be tested, instead of being forced to test larger and larger Mersenne numbers.

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