# 8951

This number is a prime.

The prime 8951 is the number of ways to choose 20 arithmetic operators (call them c1, c2, ..., c20) each either a * or / sign, so that 1 c1 2 c2 3 c3, ..., c20 21 is an integer. This is the largest known prime of that form. Curiously, it is also a prime that is a sum of twin primes and their indices, and a primitive prime divisor of (3^32-1)/2. [Post]

A total of exactly 8951 "+" signs are required in writing out the partitions of the prime 23 (23 = 22 + 1 = 21 + 2 = 21 + 1 + 1 = ... = 1 + 1 + ... + 1 + 1). Note that 8 + 9 + 5 + 1 = 23. [Beedassy]

(There is one curio for this number that has not yet been approved by an editor.)

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