Collaborative prime number searching website PrimeGrid has announced its most recent discovery: on 14th September, user Tom Greer discovered a new pair of twin primes (primes which differ by 2), namely:
\[2996863034895 \times 2^{1290000} \pm 1\]
Found using PrimeGrid’s Sophie Germain Prime search, the new discoveries are 388,342 digits long, smashing the previous twin prime record of 200,700 digits.
PrimeGrid is a collaborative project (similar to GIMPS, which searches for specifically Mersenne Primes) in which anyone who downloads their software can donate their unused CPU time to prime searching. It’s been the source of many recent prime number discoveries, including several in the last few months which rank in the top 160 largest known primes.
The University of Tennessee Martin’s Chris Caldwell maintains a database of the largest known primes, to which the new discovery has been added.
Further Reading
Press release from PrimeGrid (PDF)
The List of Largest Known Primes
PrimeGrid website
The new twin primes’ entries on the List of Largest Known Primes: n+1, n-1