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Old 2007-06-17, 20:47   #1
tha
 
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Default found this factor

[Sun Jun 17 07:24:58 2007]
P-1 found a factor in stage #2, B1=420000, B2=11970000.
UID: Tha/test25, M33604049 has a factor: 136310731051936404841226250672413144328777911

45 digits, but not checked if it is composite.
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Old 2007-06-17, 21:22   #2
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294119824093630492221527 × 463453055134913541793
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Old 2007-06-18, 17:18   #3
ewmayer
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463453055134913541793 = 1+2*p*k, with k = 24*3*17*17387*486037,
294119824093630492221527 = 1+2*p*k, with k = 44683*179057*546977,

that's why the composite factor was found in stage 2, but neither of the prime factors popped out after stage 1 - each has a largest factor of k slightly above the stage 1 primes bound.

Apparently Prime95 only does 2 GCDs, one at the end of each stage - a GCD done when stage 2 reached any prime >= 486037 would have revealed the smaller factor, and one done at any p >= 546977 (much smaller than the stage 2 upper bound that was used) would have revealed both.

But stage 2 primes are cheap and GCDs expensive...

Last fiddled with by ewmayer on 2007-06-18 at 17:22
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Old 2007-06-18, 19:44   #4
xilman
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Quote:
Originally Posted by ewmayer View Post
463453055134913541793 = 1+2*p*k, with k = 24*3*17*17387*486037,
294119824093630492221527 = 1+2*p*k, with k = 44683*179057*546977,

that's why the composite factor was found in stage 2, but neither of the prime factors popped out after stage 1 - each has a largest factor of k slightly above the stage 1 primes bound.

Apparently Prime95 only does 2 GCDs, one at the end of each stage - a GCD done when stage 2 reached any prime >= 486037 would have revealed the smaller factor, and one done at any p >= 546977 (much smaller than the stage 2 upper bound that was used) would have revealed both.

But stage 2 primes are cheap and GCDs expensive...
As is factoring small composite integers.


Paul
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Old 2007-06-18, 19:56   #5
ewmayer
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Quote:
Originally Posted by xilman View Post
As is factoring small composite integers.
True, but irrelevant to the argument that 99% of the stage 2 runtime ended up being unnecessary in this instance.
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