20220701, 08:05  #1 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
6771_{8} Posts 
New Mixed Proth Theorem
See PrimeGrid New Sierpinski Problem and Mixed Sierpinski Theorem
For every odd k < 78557, there is an n such that 2^n > k and either k*2^n+1 or 2^n+k (or both) is prime For the k*2^n+1 case, there are only 5 k's < 78557 remain with no known k with 2^n > k: {23971, 45323, 50777, 50873, 76877}, see http://boincvm.proxyma.ru:30080/test...ob_problem.php, together with the 5 remain k's in the original Sierpinski: {21181, 22699, 24737, 55459, 67607}, there are 10 remain k's And there are known primes of the form 2^n+k with 2^n > k for these k: Code:
2^28+21181 2^26+22699 2^11152+23971 (certificate) 2^17+24737 2^47+45323 2^61+50777 2^55+50873 2^746+55459 2^16389+67607 (certificate) 2^37+76877 You can try the new mixed Riesel problem, i.e. for odd k < 509203, is there always an n such that 2^n > k and either k*2^n1 or 2^nk (or both) is prime? 
20220710, 22:20  #2  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Quote:
For k = 2293, we already known that 2293*2^129184311 is prime, for k = 14347, we have a prime 14347*2^259971 and a PRP 2^13009914347, thus we known that all odd k < 25000 have a prime, but can this "New Mixed Riesel Problem" become a theorem? 

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