This page contains 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, (2^{11}−1). The next Mersenne number however, which is 2^{13}−1 or 8,191, is prime.- It is also the smallest strong pseudoprime to base 2.
- In the fast-growing hierarchy, it is equal to
*f*_{2}(8)−1 and*f*_{3}(2)−1.

- 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
**(2**.^{13}+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
**(2**= 43,691. The corresponding Mersenne number is equal to^{17}+1)/3**2**= 131,071 or M^{17}−1_{17}. 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
**(2**= 174,763. The corresponding Mersenne prime is equal to^{19}+1)/3**2**= 524,287 or M^{19}−1_{19}. 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 M_{M19}or M_{524,287}.**231,733,529**is the smallest prime factor of the composite double Mersenne number M_{M17}.- 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
**(2**= 715,827,883.^{31}+1)/3 **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 M_{M13}.**295,257,526,626,031**is the smallest prime factor of the composite double Mersenne number M_{M31}.**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
**(2**= 768,614,336,404,564,651.^{61}+1)/3 - \(2^{107}-1\) 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
**(2**= 56,713,727,820,156,410,577,229,101,238,628,035,243.^{127}+1)/3 - 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
**2**= 170,141,183,460,469,231,731,687,303,715,884,105,727.^{127}−1 - \(2^{521}-1=512*2^{512}-1 \approx 6.8647976601306097 \times 10^{156}\) 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
*f*_{2}(512)−1.