Definition:Twin Primes

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Definition

Twin primes are pairs of prime numbers whose difference is $2$.


Sequence

The sequence of twin primes begins:

$3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, \ldots$


Also known as

A pair of twin primes is also known as a prime pair or prime-pair.


Examples

Pair of Large Twin Primes

The integers defined as:

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

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


Pair of Titanic Twin Primes

The integers defined as:

$190 \, 116 \times 3003 \times 10^{5120} \pm 1$

are a pair of titanic twin primes.


That is:

$570 \, 918 \, 347 \paren 9_{5820}$

and:

$570 \, 918 \, 348 \paren 0_{5819} 1$


where $\paren a_b$ means $b$ instances of $a$ in a string.


Example: $2 \, 003 \, 663 \, 613 \times 2^{195 \, 000} \pm 1$

The integers:

$2 \, 003 \, 663 \, 613 \times 2^{195 \, 000} \pm 1$

are twin primes.


Also see


Sources

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