 mersenneforum.org New Mixed Proth Theorem
 Register FAQ Search Today's Posts Mark Forums Read 2022-07-01, 08:05 #1 sweety439   "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 67718 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 And hence the new mixed Proth (Sierpinski) problem is now a theorem!!! 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^n-1 or 2^n-k (or both) is prime?   2022-07-10, 22:20   #2
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

72×73 Posts Quote:
 Originally Posted by sweety439 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^n-1 or 2^n-k (or both) is prime?
For the Riesel side, see the attached file for odd k < 25000

For k = 2293, we already known that 2293*2^12918431-1 is prime, for k = 14347, we have a prime 14347*2^25997-1 and a PRP 2^130099-14347, thus we known that all odd k < 25000 have a prime, but can this "New Mixed Riesel Problem" become a theorem?
Attached Files New Mixed Riesel.txt (117.9 KB, 7 views)  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post ewmayer Computer Science & Computational Number Theory 6 2014-05-14 21:03 ATH Math 9 2011-02-15 19:09 Bill Bouris Conjectures 'R Us 4 2009-04-07 13:25 Dougy Math 15 2008-01-30 21:17 Cyclamen Persicum Math 1 2004-04-20 04:54

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