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
- 1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.) ... (previous) ... (next): $\text I$: The Series of Primes: $1.4$ The sequence of primes
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1 \cdotp 90195 \ldots$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): twin primes
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.16$: The Sequence of Primes
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1 \cdotp 90216 \, 054 \ldots$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): twin primes (prime pair)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): twin primes (prime pair)
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $7$: Patterns in Numbers: Fermat
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): twin primes