# 431

This number is a prime.

Divide the prime number 431 by 510 to obtain an excellent approximation to log_{10}(7). [Kulsha]

In addition to 431 and 433 being twin primes, both the 431st and the 433rd Fibonacci numbers are prime. [Dobb]

Polaris (the North Star) was thought to be about 431 light-years from Earth according to astrometric measurements of the Hipparcos satellite. It is now known to be much closer.

n! is divisible by the sum of the decimal digits of n! for all numbers n from 1 to 431. Note that 431 is prime also. [Gupta]

2*3*5*...*prime(431-1) = prime(431)-1 (mod prime(431)). Note that 431 is the largest known prime with this property and there exist only one other known such prime. [Firoozbakht]

The smallest prime of form 2^n-n^2 for n a composite number. [Loungrides]

Signals travel along an alpha motor neuron in the spinal
cord 431 km/h; the fastest transmission in the human body,
according to *Discover* magazine.

If A = 3, B = 7, C = 11, ... , Z = 223, using the Gaussian prime alphabet, then 'PRIME' is a Gaussian prime. [Homewood]

431 is the only 3-digit prime number that is an anagram of the first 3 digits of π (3.14). [Jacobs]

The Council of Ephesus convened near present-day Selçuk in 431.

0^0 + 1^1 + 2^2 + 3^3 + 4^4 + ... + 429^429 + 430^430 + 431^431 is a titanic prime (1136-digits) if we allow 0^0 = 1. [Tolgede]

The Peloponnesian War started in 431 BC.