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 Jean Penné 2018-05-06 15:24

Status for k=138847

[QUOTE=paulunderwood;486979]My-my! That is a large domain to search and so few candidates left after sieving. Good luck with finding a big prime![/QUOTE]

Thank you, Paul, for encouraging me!
I am continuing this search on this k value because of the prime 138847 *2^1283793-1 I discovered in April 2003, using the very first LLR version (without IBDWT)! This prime was then the 10th rank in larger known primes.
But, in fact, I was then very, very lucky!
Indeed, the Nash weight for k=138847 is 29, which correspond to a value of Ck- = 0.0476 of the Gallot weight (Cf the paper by Yves Gallot "On the number of primes in a sequence").
Then, it it is interesting to apply the formula given by Yves in page 6 of his work, to compute the expected number of primes found up to exponent N :

Pi(N) ~ Ck-*log2[(1.5*N+log2(k))/(1+log2(k))]

Then, I find :

Pi(1400000) ~ 0.80 (but there are 2 primes in this range).
Pi (10000000) ~ 0.94
Pi(180000000) ~ 1.13
Pi(360000000) ~ 1.16

The only thing we are sure is 138847 is not a Riesel number, n = 33 and n = 1283793 yielding primes but the chance to find larger primes is rather small...
Nevertheless, I hope to be lucky a second time...

Best Regards,
Jean

 pepi37 2018-05-06 22:40

[QUOTE=Jean Penné;487083]

The only thing we are sure is 138847 is not a Riesel number, n = 33 and n = 1283793 yielding primes but the chance to find larger primes is rather small...
Nevertheless, I hope to be lucky a second time...

Best Regards,
Jean[/QUOTE]

I would like to ask : Riesel number as Proth number by definition has no prime at all. So weight of both types of number in that case would be 0.
So my question is: can for example candidate have weight 30 and still not to produce prime never , or prime exist, but since weight is too low, and position of prime is random, prime cannot be found so quickly.

 Jean Penné 2018-05-11 15:42

[QUOTE=pepi37;487102]I would like to ask : Riesel number as Proth number by definition has no prime at all. So weight of both types of number in that case would be 0.
So my question is: can for example candidate have weight 30 and still not to produce prime never , or prime exist, but since weight is too low, and position of prime is random, prime cannot be found so quickly.[/QUOTE]

The Nash weight of a k value is obtained while testing the divisibility by a finite number of primes ; a zero result proves that the set of divisors is, or contains a covering set, so the k value is a Riesel or Sierpinski number.
On the other part, a low weight value for k can be found while there exists a covering set which can be huge, or even, infinite... This possibility remains while no prime are found for this k!

Regards,
Jean

 pepi37 2018-05-11 18:12

[QUOTE=Jean Penné;487414]The Nash weight of a k value is obtained while testing the divisibility by a finite number of primes ; a zero result proves that the set of divisors is, or contains a covering set, so the k value is a Riesel or Sierpinski number.
On the other part, a low weight value for k can be found while there exists a covering set which can be huge, or even, infinite... This possibility remains while no prime are found for this k!

Regards,
Jean[/QUOTE]

So regardless fact that some k can have positive nash weight, that K does not have any prime. That is good to know

 Jean Penné 2018-05-21 14:54

Status for k=138847

Hi,
k=138847 is now tested up to n=10,222,017(3,077,139 decimal digits) ; no new prime, continuing.
Regards,
Jean

 Grotex 2018-06-24 05:29

[B]jocelynl[/B] Can I reserve k=1466501(=29*61*829)?

Greetings,
Grotex

 Grotex 2018-06-24 06:37

[QUOTE=Grotex;490398][B]jocelynl[/B] Can I reserve k=1466501(=29*61*829)?

Greetings,
Grotex[/QUOTE]

Nash weight of 1466501 : 119

 Grotex 2018-06-27 10:00

[QUOTE=Grotex;490398][B]jocelynl[/B] Can I reserve k=1466501(=29*61*829)?

Greetings,
Grotex[/QUOTE]

Seems that I am not welcomed...
Then I give up.

 VBCurtis 2018-06-27 13:07

Nobody objects to your request; you posted a question to a member who checks in perhaps 3-4 times a year. You shouldn't expect an answer in a week!

 Jean Penné 2018-07-02 13:05

Status for k=138847

Hi,
k=138847 is now tested up to n=10,508,433(3,163,359 decimal digits) ; no new prime, continuing.
Regards,
Jean

 Jean Penné 2018-08-28 09:30

Status for k=138847

Hi,
k=138847 is now tested up to n=10,901,697(3,281,743 decimal digits) ; no new prime, continuing.
Regards,
Jean

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