Prime Curios!: 431

431
(another Prime Pages' Curiosity)

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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) is 431 light-years from Earth, according to astrometric measurements of the Hipparcos satellite.

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]

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