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This page contains Mersenne-related numbers.

List of Mersenne-related numbers Edit

  • 127 (one hundred twenty-seven) is a positive integer equal to \(2^{2^3-1}-1\). It is notable in computer science for being the maximum value of an 8-bit signed integer. It is the 4th Mersenne prime.
  • The Lucas–Lehmer primality test, which is used for finding the largest known primes, gives 194 after two iterations.
  • 496 (four hundred ninety-six) is the third perfect number. Its divisors are 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496.
  • 2,047 is the smallest composite Mersenne number with prime index, in this case, (211−1). The next Mersenne number however, which is 213−1 or 8,191, is prime.
  • The number 13 is one of only nine known numbers holding all three conditions of the New Mersenne conjecture. The corresponding Wagstaff prime is equal to (213+1)/3 = 2,731.
  • 8,128 (eight thousand one hundred twenty-eight) is the fourth perfect number.
  • \(8,191=2^{13}-1\) is the smallest Mersenne prime which is not an exponent of another Mersenne prime.
    • It is also the largest known number which is a repunit with at least three digits in more than one base. The Goormaghtigh conjecture states that 31 and 8,191 are the only two numbers with this property.
  • The number 17 is one of only nine known numbers holding all three conditions of the New Mersenne conjecture. The corresponding Wagstaff prime is equal to (217+1)/3 = 43,691. The corresponding Mersenne number is equal to 217−1 = 131,071 or M17. It is also the 6th known Mersenne prime.
  • The number 19 is one of only nine known numbers holding all three conditions of the New Mersenne conjecture. The corresponding Wagstaff prime is equal to (219+1)/3 = 174,763. The corresponding Mersenne prime is equal to 219−1 = 524,287 or M19. It is also the 7th known Mersenne prime.
  • 33,550,336 (thirty-three millions five hundred fifty thousands three hundred thirty-six) is the fifth perfect number.
  • 62,914,441 is the smallest prime factor of the composite double Mersenne number MM19 or M524,287.
  • 231,733,529 is the smallest prime factor of the composite double Mersenne number MM17.
  • The number 31 is one of only nine known numbers holding all three conditions of the New Mersenne conjecture. The corresponding Wagstaff prime is equal to (231+1)/3 = 715,827,883.
  • 2,147,483,647 is a positive integer equal to \(2^{31} - 1 = 2^{2^5 - 1} - 1\). It is notable in computer science for being the maximum value of a 32-bit signed integer, which have the range [-2147483648, 2147483647]. It is also a prime number (conveniently for cryptographers), and so the 8th Mersenne prime.
    • Its full name in English is "two billion/milliard one hundred forty-seven million four hundred eighty-three thousand six hundred forty-seven," where the short scale uses "billion" and the long scale uses "milliard."
    • The number 31 is one of only nine known numbers holding all three conditions of the New Mersenne conjecture.
  • 8,589,869,056 is the sixth perfect number. Furthermore, it is the largest known perfect number not containing digit '4'.
  • 338,193,759,479 is the smallest prime factor of the composite double Mersenne number MM13.
  • 295,257,526,626,031 is the smallest prime factor of the composite double Mersenne number MM31.
  • 9,007,199,254,740,991 is a positive integer equal to \(2^{53} - 1\). It is notable in computer science for being the largest odd number which can be represented exactly in the double floating-point format (which has a 53-bit significand).
    • Its prime factorization is 6,361 × 69,431 × 20,394,401.
  • The number 61 is one of only nine known numbers holding all three conditions of the New Mersenne conjecture. The corresponding Wagstaff prime is equal to (261+1)/3 = 768,614,336,404,564,651.
  • \(2^{107}-1\) is the largest known Mersenne prime not containing the digit '4'. Its full decimal expansion is 162,259,276,829,213,363,391,578,010,288,127.
  • It has been conjectured that no number larger than 127 holds all three conditions of the New Mersenne conjecture. The corresponding Wagstaff prime is equal to (2127+1)/3 = 56,713,727,820,156,410,577,229,101,238,628,035,243.
  • It has been conjectured that no number larger than 127 holds all three conditions of the New Mersenne conjecture. The corresponding Mersenne prime is equal to 2127−1 = 170,141,183,460,469,231,731,687,303,715,884,105,727.
  • \(2^{521}-1=512*2^{512}-1 \approx 6.8647976601306097 \times 10^{156}\) is the largest known Mersenne prime which is also a Woodall number. There are no other such numbers smaller than \(2^{549,755,813,927}-1\).
    • Its full decimal expansion is 6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151.
    • In the fast-growing hierarchy, it is equal to f2(512)−1.

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