SophieGermainPrimeQ

Determines if the given number is a Sophie Germain prime, or not

ResourceFunction["SophieGermainPrimeQ"][p]

gives True if p is a Sophie Germain prime and False otherwise.

Details and Options

A Sophie Germain prime is a prime number q, where 2q+1 is also prime.

The prime number 11 is a Sophie Germain prime, because both 11 and 23 (2·11+1) are primes:

In[1]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/Function/\ SophieGermainPrimeQ"][11]$

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The number 14 is not a Sophie Germain prime, because it is not a prime itself, even though 29 (2·14+1) is a prime number:

In[2]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/Function/\ SophieGermainPrimeQ"][14]$

Out[2]=

The number 7 is not a Sophie Germain prime, because 15 (2·7+1) is not prime:

In[3]:=

$ResourceFunction[ "https://www.wolframcloud.com/obj/arnoudb/DeployedResources/Function/\ SophieGermainPrimeQ"][7]$

Out[3]=