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Old 2008-10-13, 00:52   #1
Apprentice Crank
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Mar 2006

2·227 Posts
Default Sophie Germains, multiple n-ranges, future of TPS

This thread is for discussing a possible search for Sophies and searching a range of both n and k for twins.

Recently, a couple of people have asked me about doing a search for both sophies and twins for n=500K. Doing so means that there's a greater chance of finding either a sophie or a twin, but one problem is that the chance of finding a twin in a range decreases the higher you sieve. As a guide, there are about 500,000 candidates left after triple-sieving a range of 10G to p=1T. Continuing to p=1000T with a twin-sieve would leave 320,000 candidates remaining, while continuing to p=1000T with a triple-sieve would leave only 256,000 candidates remaining. Some of those candidates eliminated with a triple sieve but not eliminated with a twin sieve may have been twins.

Another suggested idea came up in this rather long thread:

It was suggested that TPS search for a range of n with a smaller k range instead of searching a large k-range with a fixed n. The advantage is that the low k-candidates in a variable n-range are faster to test than those with a fixed n, while a disadvantage is that sieving won't be as efficient.

If you want TPS to also look for sophies, I'd welcome suggestions for a suitable k-range for triple sieving n=500K. For those who want to try triple-sieving a test range to get the idea of how it works and how much time and RAM is required, download David Underbakke's Twingen software at:
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