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Message boards : Extended Sierpinski Problem : Details for "Sierpinski Problem ESP/PSP/SoB Sieve"

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Vitaly

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Message 89878 - Posted: 20 Nov 2015 | 4:29:27 UTC

Could you please explain what does mean:
there were found 671 factors in range "51P - 52P"?

Does this mean that there are 671 Sierpinski nubers which are not primes in range "51P - 52P" or something else?

Thank you.

JimB
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Project developer

Joined: 4 Aug 11
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Message 89883 - Posted: 20 Nov 2015 | 12:12:40 UTC - in response to Message 89878.

Could you please explain what does mean:
there were found 671 factors in range "51P - 52P"?

Does this mean that there are 671 Sierpinski nubers which are not primes in range "51P - 52P" or something else?

Thank you.

It means that looking at primes in the range 51P-52P (51,000,000,000,000,000 - 52,000,000,000,000,000) there were 671 candidates for which one of those primes was a factor. Any candidate that has a factor is by definition not prime. Those candidates will be removed from the sieve file and will never be tested with LLR. This doesn't have an immediate effect on our site because we're currently testing candidates with n < 10M while the sieving is taking place on n between 10M and 50M. When we run out of candidates below 10M then the new sieve will be used.

Vitaly

Joined: 24 Sep 12
Posts: 59
ID: 173343
Credit: 13,381,699
RAC: 26,894

Message 89900 - Posted: 21 Nov 2015 | 1:39:43 UTC - in response to Message 89883.

Could you please explain what does mean:
there were found 671 factors in range "51P - 52P"?

Does this mean that there are 671 Sierpinski nubers which are not primes in range "51P - 52P" or something else?

Thank you.

It means that looking at primes in the range 51P-52P (51,000,000,000,000,000 - 52,000,000,000,000,000) there were 671 candidates for which one of those primes was a factor. Any candidate that has a factor is by definition not prime. Those candidates will be removed from the sieve file and will never be tested with LLR. This doesn't have an immediate effect on our site because we're currently testing candidates with n < 10M while the sieving is taking place on n between 10M and 50M. When we run out of candidates below 10M then the new sieve will be used.

Do not exactly understand "there were 671 candidates for which one of those primes was a factor"

Do you mean that all 671 numbers have a factor and hence are not primes?

JimB
Volunteer moderator
Project developer

Joined: 4 Aug 11
Posts: 903
ID: 107307
Credit: 964,756,678
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Message 89910 - Posted: 21 Nov 2015 | 11:48:30 UTC - in response to Message 89900.

Out of all the candidates in the sieve, 671 of them had a factor somewhere between 51P-52P. They were almost certainly all different factors rather than the same one. The important thing is that those candidates are proven composite (not prime) and will be removed from further consideration. Any factor returned is tested by the validator to make sure it really is a factor and then it's tested again by me later before the now-known-composite candidate is removed from the sieve.

Here are the first few factors in that range:

51000761915701909 is a factor of 163187*2^12490935+1 51001288191895927 is a factor of 200749*2^40718586+1 51005036548895321 is a factor of 238411*2^46965396+1 51006857875746229 is a factor of 99739*2^49878210+1 51010368588514211 is a factor of 163187*2^29439495+1

In the notation we use: p is a factor of k*2^n+1

Those candidates on the right hand side are now proven composite, so they don't need to be tested by LLR. We search p values sequentially and right now the candidate list is for n values of 10M (10,000,000) to 50M (50,000,000). You can see that all the candidates show an n value in that range.

Vitaly

Joined: 24 Sep 12
Posts: 59
ID: 173343
Credit: 13,381,699
RAC: 26,894

Message 89935 - Posted: 22 Nov 2015 | 8:42:35 UTC - in response to Message 89910.

It is clear now.
Thank you.

Message boards : Extended Sierpinski Problem : Details for "Sierpinski Problem ESP/PSP/SoB Sieve"