Even the options are prime

Number Theory Level 3

Let a , b , c \large a,b,c be prime numbers such that they satisfy the following properties:-

1. a < b < c \large 1. a<b<c

2. a + b = c \large 2.a+b = c

How many triplets of ( a , b , c ) \large (a,b,c) are possible?

101 More than 101 11 2

Ravneet Singh by Ravneet Singh , 30, India

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1 solution

Note that a a has to be 2 2 for parity reasons. This is equivalent to finding the number of twin primes . It is conjectured that there are infinitely many twin primes so the answer is more than 101 101 .

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