The other day I needed to test some software with a moderately large prime number as input. The first thing that came to mind was 8675309. This would not be a memorable number except it was in the chorus of the song 867-5309/Jenny.

It turned out that 8675309 was too large. The software would take too long to run with this input. It occurred to me that while I could quickly come up with a prime number with seven digits, nothing came to mind immediately with four, five, or six digits. This post will share some numbers I came up with.

Symmetry

Symmetry makes things more memorable, so one thing to try is finding primes with a symmetric pattern of digits. The numbers 13331 and 18181 are examples of palendromic primes, prime numbers that read the same forwards and backwards. You can find more palendromic primes here.

This won’t help find memorable primes with four or six digits because all palendromic numbers with an even number of digits are divisible by 11.

Consecutive digits

The number 123457 is a memorable six-digit prime, being the first seven digits with six removed. Maybe there are other variations that are memorable. (Or the you find memorable; memorability is subjective.)

Consecutive digits of π

A variation on looking for primes in consecutive integers is to look for primes in consecutive digits of another number, the most famous being π.

314159 is a pi prime, and it’s memorable if you know the value of π to at least six digits. This won’t help us find a memorable four-digit prime since 3141 is divisible by 9.

Years

The last prime number year that we lived through was 2017, and the next, God willing, will be 2027.

1999 was a prime. It was also the title of a song that came out in 1982, one year after the song 867-5309/Jenny.

Powers of 2

Programmers will likely recognize 65536 as 2¹⁶, and 65537 is prime, the largest known Fermat prime.

Whether something is memorable depends on what previous memories you can connect it to. Many people are familiar with powers of 2 and would find primes of the form 2^k ± 1 memorable.

The number 2¹³ = 8192 is not as familiar as 2¹⁶ = 65536, but 8191 is a four-digit prime.

Summary

Having written this post, the following responses are likely what would come to mind if you asked me for primes of various lengths.

1. 7
2. 97
3. 997
4. 1999
5. 18181
6. 314159
7. 8675309

The post Memorable Primes first appeared on John D. Cook.