23451 · 2^3739388 + 1

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Jeppe Stig Nielsen writes (15 May 2023):  (report abuse)

First prime of form 23451*2^{2*m} + 1. This contributes to the proof of the following case of the "Liskovets-Gallot conjectures": Theorem: 66741 is the smallest positive k with k==3 (mod 6) such that no prime of form k*2^n + 1 has an even exponent n. Proof: To see that 66741 has this property, consider the covering set { 5, 7, 13, 17, 241 }. And to see that 66714 is smalles with this property, run through all smaller k with k==3 (mod 6) and find at least one prime of form k*2^{2*m} + 1; the present prime (with k=23451) is the largest one encountered during that calculation.

Verification data:

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