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523 is a prime number from 501-600. 523 has 2 factors, 1 and 523. It is the 99th prime number, and the fourth prime number from 501-600.

Proofs

  • Yes — 523 can be divided by 1.
  • No — 523 cannot be divided by 2-522.
  • Yes — 523 can be divided by 523.


As an Exponent of Mersenne Number

2523 - 1 is not a prime number. The divisor has 69 digits[1]:

160188778313202118610543685368878688932828701136501444932217468039063

Relationship with other odd numbers

The numbers before

  • The previous prime number is 521.
    • There are no odd numbers between 521 and 523. As a result, they are twin primes.
  • The previous prime number before 521 is 509.
    • 511 is divisible by 7, while 517 is divisible by 11. Both numbers are composite.

The numbers after

  • The next prime number is 541. There is a tremendous 18-number prime gap between 523 and 541. All numbers between them are composite. In particular:
    • 527 is the product of 17 and 31.
    • 529 is the square of 23.
    • 533 is the product of 13 and 41.
    • 539 can be factored as 72 x 11.
    • 531 and 537 are divisible by 3, and 535 is visibly divisible by 5.
  • 547 is the next prime number after 541.

References

  1. http://www.mersenne.org/report_exponent/?exp_lo=523&exp_hi=523&full=1
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