431

This number is a prime.

+ Divide the prime number 431 by 510 to obtain an excellent approximation to log10(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.

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