perplexus.info :: Just Math : Prime Number Arithmetic

Prime Number Arithmetic (Posted on 2004-11-19)

Find all primes p such that 2^p + p^2 is also prime.

Prove there are no others.

Submitted by Erik O.

Rating: 4.1250 (8 votes)

Solution: (Hide)

I haven't proved it for certain, but it appears that after 3, the results for all primes end up evenly divisible by 3...

1 => 3
3 => 17
5 => 57
7 => 177
11 => 2169
13 => 8361
.
.
.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2022-01-08 20:50:39
solution using mods	Brent	2007-02-05 17:44:14
Solution with partial proof	Michael	2004-11-26 21:25:21
Concurrence	Steve Herman	2004-11-21 12:22:22
re: Solution with mini-proof	owl	2004-11-20 01:26:34
re: Solution with mini-proof, Well done.	Dustin	2004-11-19 23:09:58
Solution with mini-proof	SteveH	2004-11-19 21:55:13

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