Can you find the no ?

Number Theory Level 2

If p is a prime and ( p 2 p^2 +3) is also a prime then ,find the no. of numbers that p can assume .

3 can't say 1 2

Tanmay Goyal by tanmay goyal , 21, India

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3 solutions

Anshul Sanghi
Feb 3, 2015

only 2 will satisfy the equation . only 2 is an even prime number. any other prime square will be odd and adding 3 will make it even which could not be even.

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Sauditya Yo Yo
Jan 30, 2015

if p is odd , p^2 +3 is even as p <p^2+3 therefore p=2

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Yes ,there is only 1 even prime that is 2..which when put in p^2 +3 yeilds 7 which is a prime...all other primes are odd..and yeild only an even no. When put in p^2+3 ....So the no. of such primes is 1

tanmay goyal - 6 years, 4 months ago
Noel Lo
Apr 28, 2015

p=2 and p 2 + 3 = 4 + 3 = 7 p^2+3 = 4+3=7 which is also a prime.

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