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 Register FAQ Search Today's Posts Mark Forums Read  2016-06-17, 21:04 #34 lalera   Jul 2003 26316 Posts hi, here are the results for near-cube numbers done with cksieve v3.1.7 and openpfgw b=74, n=1 to 10000 (74^27+1)^3-2 (74^2564-1)^3-2 (74^9291+1)^3-2   2016-06-18, 14:53 #35 lalera   Jul 2003 13×47 Posts hi, here are the results for near-cube numbers done with cksieve v3.1.8 and openpfgw b=6, n=1 to 10000 (6^1-1)^3+2 (6^3-1)^3+2 (6^2+1)^3-2 (6^3+1)^3-2 (6^44+1)^3+1*(-2) (6^48+1)^3+1*(-2) (6^57+1)^3+1*(-2) (6^188+1)^3+1*(-2) (6^624-1)^3-1*(-2) (6^738+1)^3+1*(-2) (6^1284-1)^3-1*(-2) (6^1571-1)^3-1*(-2) (6^2324-1)^3-1*(-2) (6^2907-1)^3-1*(-2) (6^5418-1)^3-1*(-2) (6^6161-1)^3-1*(-2) - b=12, n=1 to 10000 (12^2-1)^3+2 (12^2+1)^3-2 (12^3+1)^3-2 (12^24-1)^3-1*(-2) (12^122-1)^3-1*(-2) - b=74, n=1 to 10000 (74^27+1)^3+1*(-2) (74^9291+1)^3+1*(-2)   2016-06-18, 16:56 #36 Batalov   "Serge" Mar 2008 Phi(4,2^7658614+1)/2 17×563 Posts And (2^471043+1)^3-2 is prime!   2016-06-18, 17:37   #37
paulunderwood

Sep 2002
Database er0rr

53×73 Posts Quote:
 Originally Posted by Batalov And (2^471043+1)^3-2 is prime!
Congrats How about near-quartics? With a little factorisation, a CHG proof could be done    2016-06-18, 17:58 #38 Batalov   "Serge" Mar 2008 Phi(4,2^7658614+1)/2 17×563 Posts No, that would be a lot of factorization! Doing just one additional % (up to still unmanageable 26% CHG of this size) is getting > 3882 additional digits of factors - that's unrealistic. Besides, there exist tons of near-4th-powers primes (x4+1) - they are Generalized Fermats. For this near-cube, btw, to avoid K-P proof, we observe that p+1 has a factor of 5209 * which pushes the log(factored(N+1))/log(N) strictly over 1/3. ____________________ * EDIT: ... and 8968913743 Last fiddled with by Batalov on 2016-06-18 at 18:18   Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post rogue And now for something completely different 253 2021-10-15 08:39 rogue And now for something completely different 294 2021-08-30 08:07 JeppeSN And now for something completely different 27 2018-04-12 14:20 flava Open Projects 18 2010-12-04 05:24 Unregistered Math 8 2005-04-27 00:55

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