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Message boards : Sophie Germain Prime Search : The Exponent

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Gary Craig
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Message 73588 - Posted: 18 Feb 2014 | 5:55:00 UTC

I'm curious as to the history of how the exponent was/is chosen for the various SGS (and twin prime search) ranges that we've searched over the years. I believe that TPS (before my time) searched n=333333, and SGS mostly did n=666666 and now n=1.29M. I believe the immediate answer is that there had been heavy sieving done, making LLR efficient to run on those ranges. But that of course just begs the question as to why those ranges had been heavily sieved. Is there something "special" about those n's (other than the repeated digits, of course), or would it be equally valid/productive to search n=314159 or n=987987 or n=1234567? Assuming the sieving were done for those n, of course.

I did find a board post from Lennart saying (in part) that n=1.29M keeps us under a particular FFT size threshold.

Just curious.

--Gary
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87*2^3496188+1 is prime! (1052460 digits)
4 is not prime! (1 digit)

Honza
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Message 73590 - Posted: 18 Feb 2014 | 8:46:58 UTC

One reason is that you mentioned, particular FFT size threshold.

The other reason is that we want to keep SGS in Top5000 as long as possible, which needs to be considered together with PPSe progress.
New SGS primes are entering ~1700 place and pushing all PPSe primes down (entering 3000 - 3500). Once PPSe crosses 1290k (with leading edge being around 1248k), it will start pushing all SGS down.

btw, TPS was done also for n=195000.
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JeppeSN

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Message 90293 - Posted: 9 Dec 2015 | 0:44:58 UTC

Right now, the prime:

835738017*2^1290000 - 1 (2012 July 14)

is ranked 5350 on Caldwell's list, and the prime:

2400254545845*2^1290000 - 1 (2015 December 8)

is ranked 3349 there.

Of course almost all the primes in the list in between these two are also from this project. (One user, p199, seems to start from two primes found by this project, say k*2^1290000-1 and j*2^1290000-1 (with k<j), and then see if i*2^1290000-1 is also prime, where i = j+(j-k) = 2j-k is the next member of the arithmetic progression k,j,...)

If we are lucky that one of our finds will be the lower member of a twin, or a safe prime, or a Sophie Germain prime, our exponent 1290000 is still large enough to ensure that both that prime and the associated prime are in Top 5000 in their own rights.

/JeppeSN

Message boards : Sophie Germain Prime Search : The Exponent