Related Experiment Videos
The 24th mersenne prime.
1IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598.
Summary
The largest known prime number, the 24th Mersenne prime (2^19937 - 1), was confirmed using the Lucas-Lehmer test. This discovery also identified the 24th even perfect number.
Area of Science:
- Number Theory
- Computational Mathematics
Background:
- Mersenne primes are prime numbers of the form 2^p - 1.
- Perfect numbers are positive integers equal to the sum of their proper positive divisors.
Purpose of the Study:
- To identify and verify the 24th Mersenne prime number.
- To determine the corresponding even perfect number.
Main Methods:
- The Lucas-Lehmer primality test was employed.
- Utilized an IBM 360/91 computer for calculations.
Main Results:
- The 24th Mersenne prime, M(p) = 2^19937 - 1, was confirmed.
- This prime corresponds to the 24th even perfect number: (2^19937 - 1) * 2^19936.
Conclusions:
- The Lucas-Lehmer test is effective for verifying large Mersenne primes.
- The relationship between Mersenne primes and even perfect numbers is further demonstrated.