The two numbers were discovered within a fortnight of each other by the Great Internet Mersenne Prime Search project, which has spent 12 years on the task.
The largest prime number, which has a whopping 12,978,189 digits, was discovered by a team from UCLA. The second, discovered by a computer user in Germany, has 11,185,272 digits.
The search for large prime numbers (those which can only be divided by themselves or one) was sponsored by the Electronic Frontier Foundation (EFF) as part of an effort to build a near-unbreakable encryption system.
"The EFF awards are about cooperation," said John Gilmore, EFF co-founder and project leader for the awards.
"Prime numbers are important in mathematics and encryption, but the real message is that many other problems can be solved by similar methods."
The UCLA team will receive a $100,000 prize from the EFF for breaking the 10,000,000 digit record. Further prizes are available, including $150,000 for the first 100,000,000 digit prime and $250,000 for the first 1,000,000,000 digit number.
Prime numbers are fundamental to cryptography systems, which take a large part of their strength from the difficulty in factoring primes. The larger the prime the more secure the encryption.
Scientists find world's largest prime numbers
Scientists in the US and Germany have found the two largest prime numbers ever calculated in a discovery which could dramatically increase the effectiveness of cryptographic systems.
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