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 2007-06-17, 20:47 #1 tha     Dec 2002 883 Posts 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.
 2007-06-17, 21:22 #2 Xyzzy     Aug 2002 32·5·193 Posts 294119824093630492221527 ร 463453055134913541793
 2007-06-18, 17:18 #3 ewmayer ∂2ω=0     Sep 2002 Repรบblica de Califo 22×2,939 Posts 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
2007-06-18, 19:44   #4
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

2·5·1,187 Posts

Quote:
 Originally Posted by ewmayer 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

2007-06-18, 19:56   #5
ewmayer
2ω=0

Sep 2002
Repรบblica de Califo

22×2,939 Posts

Quote:
 Originally Posted by xilman 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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