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Old 2016-06-17, 21:04   #34
lalera
 
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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
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Old 2016-06-18, 14:53   #35
lalera
 
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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)
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Old 2016-06-18, 16:56   #36
Batalov
 
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Phi(4,2^7658614+1)/2

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And (2^471043+1)^3-2 is prime!
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Old 2016-06-18, 17:37   #37
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Quote:
Originally Posted by Batalov View Post
And (2^471043+1)^3-2 is prime!
Congrats

How about near-quartics? With a little factorisation, a CHG proof could be done
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Old 2016-06-18, 17:58   #38
Batalov
 
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Phi(4,2^7658614+1)/2

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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
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