Is it infinitely many?

Number Theory Level pending

${1, 101, 10101, 1010101, 101010101, ……}$

How many number in the sequence above are primes?

1 solution

Abdeslem Smahi
Jul 14, 2015

when we have an even number of $1's$ in any number of the sequence then the number is divisible by $101$ it can be written as

if the number of $1's$ is odd so the number can be written as

so the only prime number is $101$