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-   -   69 * 2^n - 1 (https://www.mersenneforum.org/showthread.php?t=18600)

 pinhodecarlos 2015-01-08 11:52

[QUOTE=diep;391911]

RPS i assume has finished up to 2.5M by now meaning everything for 69 * 2^n - 1 up until 3.56M has been checked once.
[/QUOTE]

You are right. RPS finished k=69 to n=2.5M.

 diep 2015-02-17 02:03

Good Early Morning! Fearing my hack in tool producing what to test for 69 * 2^n - 1 has bug

3M - 4M had roughly 53892 exponents to test and range am starting now at a few cores
4M - 5M has roughly 53990 exponents to test

Sounds weird to me such "huge" range has more exponents to test.

shows both ranges sieved to 400P.

Note i might have used tad older abcd file for 3m-4m range to do this quick compare, whereas in reality i had upgraded in between testing the abcd file, so i suddenly had less to test then.

Yet i'm bit confused why this difference is there, anyone?

 VBCurtis 2015-02-17 06:27

Both ranges span 1 million, both sieved to the same level, and the number of tests differs by 100. What is it you find strange? Can you rephrase your question?

 Thomas11 2015-02-17 09:27

[QUOTE=diep;395638]
3M - 4M had roughly 53892 exponents to test
4M - 5M has roughly 53990 exponents to test
[/QUOTE]

From the latest sieve file for 3M-4M I get a slightly different number: only 53812 exponents.
And (just for comparison) for the range 5M-6M there are 53731 exponents.

As VBCurtis already mentioned: The difference is quite small and is just the typical fluctuation in the distribution of surviving exponents after sieving.

 unconnected 2015-02-17 10:30

[QUOTE=Thomas11;395649]As VBCurtis already mentioned: The difference is quite small and is just the typical fluctuation in the distribution of surviving exponents after sieving.[/QUOTE]

I've checked some exponents and all seems OK except k=5.

[CODE] 51323 1M/t17_b2_k5.npg
48098 2M/t17_b2_k5.npg
45757 3M/t17_b2_k5.npg
34694 4M/t17_b2_k5.npg
34752 5M/t17_b2_k5.npg
34774 6M/t17_b2_k5.npg
[/CODE]Why so much difference between 1M-3M and 4M-6M ranges? Usually difference no more than 5-7%. For example, for k=33:

[CODE] 45919 1M/t17_b2_k33.npg
46129 2M/t17_b2_k33.npg
46271 3M/t17_b2_k33.npg
44182 4M/t17_b2_k33.npg
43896 5M/t17_b2_k33.npg
43877 6M/t17_b2_k33.npg
[/CODE]

 pinhodecarlos 2015-02-17 10:45

First there was some kind of sieve gap and second they forgot to take out the algebraic factors from k=5.

 Thomas11 2015-02-17 11:38

[QUOTE=unconnected;395650]Why so much difference between 1M-3M and 4M-6M ranges? Usually difference no more than 5-7%. For example, for k=33:

[CODE] 45919 1M/t17_b2_k33.npg
46129 2M/t17_b2_k33.npg
46271 3M/t17_b2_k33.npg
44182 4M/t17_b2_k33.npg
43896 5M/t17_b2_k33.npg
43877 6M/t17_b2_k33.npg
[/CODE][/QUOTE]

1M-3M was sieved to p=100P, while 4M-6M has been sieved to p=400P.

The number of factors for a given sieve range (from p1 to p2) can be estimated by N1*(1-log(p1)/log(p2)), where N1 is the number of candidates at sieve level p1. Then the number of candidates surviving the sieve up to p2 should be roughly N2 = N1*log(p1)/log(p2).

By taking N1=46000 at p1=100P (=100*10^15) we get N2=44427 at p2=400P.
This makes the counts given above for k=33 (and all the other k's except k=5) quite plausible for me...

 diep 2015-02-17 14:51

Thanks for the explanations and most interesting estimation formula!

At the risk of being wrong, i tend to remember when i trial factored Wagstaff ( (2^n + 1) / 3 ) that odds dramatic low that at a reasonable large domain, less exponents would be left than in a similar domain, given the same sieve depth.

Yet quite possible that with the much tougher sieving that's needed for Riesel, that sieve depths, though impossible to do at home that deep, still aren't deep enough for statistical logics to become reality.

 diep 2015-02-21 12:53

Current status.

Everything tested once up to:

69*2^3614305-1 is not prime. LLR Res64: 09A4B35ED567A38D Time : 12454.741 sec.

 diep 2015-04-04 19:25

Everything tested once up to 3.79M

Odds ticking away there still is a new gem < 4M

 Kosmaj 2015-04-05 06:07

Hi diep,
Congrats on your dedication and a great run from n=2.5M, approaching 4M soon.

No worries about no new primes. The more composites, the more reasons to rejoice since every new test has higher and higher probability to produce a new prime! :-)

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