Pair of Large Twin Primes

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Theorem

The integers defined as:

$1\,159\,142\,985 \times 2^{2304} \pm 1$

are a pair of twin primes each with $703$ digits.


Proof


Historical Note

David Wells reports in his Curious and Interesting Numbers of $1986$ that this pair of twin primes is the largest reported on by Richard K. Guy in his Unsolved Problems in Number Theory of $1981$.

It is reported that they were discovered by A.O.L. Atkin and N.W. Rickert in $1979$.


Apparently they also discovered the pair $694\,513\,810 \times 2^{2304} \pm 1$ at around the same time.


Sources