Friday, January 17, 2025

Very Large and Easy-to-Remember Prime Numbers


There was a recent article about asking people to name a prime number. One answer was given as 2^31-1; however, the responder was asked to recite the digits. He couldn't remember the digits of 2^31-1, which are 2,147,483,647. His friend, Neil  Sloane, offered another large prime: 12,345,678,910,987,654,321. It is easy to remember because one just needs to count from 1 to 10 and then back down to 1. The original story is recounted in this Scientific American article:  These Prime Numbers Are So Memorable That People Hunt for Them.

The number cited above is found in the OEIS sequence A350153.  

Other related sequences are:

A048847, Primes formed by concatenation of first k odd numbers.

A173426, a(n) is obtained by starting with 1, sequentially concatenating all decimal numbers up to n, and then, starting from n-1, sequentially concatenating all decimal numbers down to 1.

A260343, Numbers n such that the base-n number formed by concatenating the base-n numbers 1 2 ... n-1 n n-1 ... 2 1 is prime.

A323532, Numbers k such that the decimal concatenation of the numbers from 1 up to k followed by digit reversals of the numbers from (k-1) down to 1 is a prime.

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