Status for k=138847
[QUOTE=paulunderwood;486979]Mymy! 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 *2^12837931 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 
[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. 
[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 
[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 
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 
[B]jocelynl[/B] Can I reserve k=1466501(=29*61*829)?
Greetings, Grotex 
[QUOTE=Grotex;490398][B]jocelynl[/B] Can I reserve k=1466501(=29*61*829)?
Greetings, Grotex[/QUOTE] Nash weight of 1466501 : 119 
[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. 
Nobody objects to your request; you posted a question to a member who checks in perhaps 34 times a year. You shouldn't expect an answer in a week!

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 
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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