That's very odd

Number Theory Level 3

If the difference between the ( 2017 n ) th (2017n)^\text{th} prime number and the n th n^\text{th} prime number is 17537, find the value of the ( 2017 n ) th (2017n)^\text{th} prime number?


The answer is 17539.

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Achal Jain
Jan 27, 2017

The difference between any two odd primes is divisible by 2.

But as stated the value obtained is odd. Hence one prime is even and there's only one even prime number ''2''.

Hence we find our answer as 17537+2= 17539

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Anthony Holm
Nov 22, 2016

Because the difference is odd, one of the two numbers must be even and the other odd. Since 2 is the only even prime number, the other number must be 17537+2=17539

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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