MathDB

Two primes p less than 20,000

Source: IMO LongList 1988, South Korea 6, Problem 67 of ILL

November 3, 2005

number theory unsolvednumber theory

Problem Statement

For each positive integer

k

and

n,

let

S_k(n)

be the base

k

digit sum of

n.

Prove that there are at most two primes

p

less than

20,000

for which

S_{31}(p)

are composite numbers with at least two distinct prime divisors.