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Old 2015-09-27, 04:44   #5
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Uncwilly's Avatar
Aug 2003
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Originally Posted by FloatingPoint View Post
Can anyone point me in the right direction on how to check if a 1 billion digit long number is prime?
A quick and dirty calculation estimates it would take a quad core 4GHz machine working *perfectly* for about 15.5-16 years to run a single test (provided it had enough memory, memory bandwidth, large enough cache, and other such.) on a Mersenne number. Other types of primes take longer (as I am lead to understand). A single bad bit (cosmic ray, a little over heat) and the test can fail. The FFT size is too big for current processors, IIRC, so that number is already too small (by a factor of 2 to 4). Also, I don't know if mlucas, glucas, or CUDAlucas are set to handle a number this large. I don't think the current version of Prime95 is. You would want to do ~ 1-2 years of factoring on a GPU first, then about a year's worth of P-1 with a massive amount of memory (128GB ?).
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