Problem 44385. Extra safe primes

Created by Matthew Eicholtz

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Did you know that the number 5 is the first safe prime? A safe prime is a prime number that can be expressed as 2p+1, where p is also a prime.

To celebrate Cody's Five-Year Anniversary, write a function to determine if a positive integer n is a safe prime in which the prime p (such that n=2p+1) is also a safe prime.

Examples

isextrasafe(5) = false % because 5=2*2+1 and 2 is not a safe prime
isextrasafe(23) = true % because 23=2*11+1 and 11 is also a safe prime (11=2*5+1)

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Last Solution submitted on Sep 24, 2025

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Mehmet OZC on 16 Oct 2017

15 = 2*7+1 and 7 = 2*3+1 so 15 should be a safe prime. Am I missing something?

Peng Liu on 16 Oct 2017

An (extra) safe prime number itself must be a prime number. Here, 15 is not a prime, so it is not (extra) safe prime

danteliujie on 27 Feb 2019

For case 8, x = 719;
which will lead to 44, not prime, the result should be false, but it's true now.
Am I right?

Matthew Eicholtz on 28 Feb 2019

danteliujie, x = 719 does not lead to 44.

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Problem 44385. Extra safe primes

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Problem 44385. Extra safe primes

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