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New Possible Record Prime Number Found
An anonymous reader writes "The Great Internet Mersenne Prime Search (GIMPS), a distributed computing project, has probably found a new record prime number. Two verification runs have started; no errors were found in the initial calculation. The number of primes found lately, four in just over two years, is higher than previously expected. This prime is just under 10 million digits, which means that one of the participants in the project makes a good chance to obtain his or her part of the EFF prize of $100,000 for the first prime of over 10 million digits in the coming months. In 2000, one of the Gimps participants collected the $50,000 reward offered."
Bah, show me a new non-Mersenne prime and I'll be impressed...
The Prime Number Theorem tells us that in a region of d around a large number n, there are approximately d/ln n primes. For a 9 million digit n, ln n is about 21 million, so one expects to see one prime every 21 million numbers. For example, between 10^9000000 and 1.1*10^9000000, one expects 5*10^8999991 prime numbers.
Because pure mathematics sometimes turns out to have unexpected real-world benefits. Ancient Greek mathematicians such as Apollonius of Perga studied properties of the conic sections (circles, ellipses, the parabola, the hyperbola) as pure maths with no expectation of practical gain. Two thousand years later, we found that planets move in ellipses, that projectiles follow parabolic paths, and so on. Hey presto, that ancient pure mathematics becomes useful...