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Prime Possibility Poser (Posted on 2022-11-10)

Determine, with proof, all possible values of a prime number p such that the expression given below is equal to a prime number.

No Solution Yet Submitted by K Sengupta

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Possible Solution

Comment 2 of 2 |

From Fermat Little, 2p^6= 7k+2 (for p not equal to 7)

234705 = 234703+2 = 7*33529+2.

7k+2-(7*33529+2)= 7(k - 33529), never prime.

If p=7, 2*7^6-234705 = 593, which is prime, so this is the only possible prime value.

Edited on November 10, 2022, 9:02 pm

Posted by broll on 2022-11-10 21:01:33

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