8191 (number)

← 8190 8191 8192 →
Cardinaleight thousand one hundred ninety-one
Ordinal8191st
(eight thousand one hundred ninety-first)
Factorizationprime
Divisors1, 8191
Greek numeral,ΗΡϞΑ´
Roman numeralVMMMCXCI, vmmmcxci
Binary11111111111112
Ternary1020201013
Senary1015316
Octal177778
Duodecimal48A712
Hexadecimal1FFF16

8191 (eight thousand one hundred [and] ninety-one) is the natural number following 8190, and preceding 8192. It is also known as M13.[a]

In mathematics

8191 is an odd number and the 1028th prime number.[1] It is also a Jacobsthal-Lucas number.[2] It is a palindrome and repdigit in base 2, which has 13 repeated digits of the number one.[3]

Mersenne prime

It is most notable for being a Mersenne prime.[1][4] Since it is a Mersenne prime, it can be expressed as 213 - 1.[5] And since the exponent number is prime, it is considered one.[6][7] It was discovered anonymously before 1461.

See also

Notes

  1. ↑ M13 is the mathematical notation for the 13th Mersenne prime (Mp = 2p - 1) where the exponent number is 13.

References

  1. 1 2 Vanovschi, Vitalii. "Properties of the number 8191". www.numberempire.com. Retrieved 2026-08-23.
  2. ↑ Sloane, N. J. A. (ed.). "Sequence A014551 (Jacobsthal-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ↑ "Number 8191 - Properties & Facts | NumberWorld". numberworld.info. Retrieved 2026-08-23.
  4. ↑ Friedman, Erich. "What's Special About This Number?". Retrieved 2026-08-23.
  5. ↑ Roggero, Pier Francesco; Nardelli, Michele; Di Noto, Francesco (2012-12-14). Study on the Perfect Numbers and Mersenne's Prime with New Developments: Possible Mathematical Connections with Some Sectors of String Theory (PDF). Retrieved 2026-08-23.
  6. ↑ MacDougall, Jim (March 2003). "Mersenne composites and cyclotomic primes". The Mathematical Gazette. 87 (508): 71–75. doi:10.1017/S0025557200172122. ISSN 0025-5572.
  7. ↑ Sloane, N. J. A. (ed.). "Sequence A000668 (Mersenne primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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