Definition:Thabit Prime
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Definition
A Thabit prime is a Thabit number which is prime.
Sequence
The sequence of Thabit primes begins:
- $2, 5, 11, 23, 47, 191, 383, 6143, 786 \, 431, 51 \, 539 \, 607 \, 551, \ldots$
These correspond to the following values of $n$ in their generating expression $3 \times 2^n - 1$:
- $0, 1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, \ldots$
Also known as
A Thabit prime is also known as a 321 prime, from its form: $3$ times $2$ to the $n$th minus $1$.
Some sources give his name in full, or a rendition of it: Thâbit ibn Kurrah prime.
The shorter form is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Also see
- Results about Thabit primes can be found here.
Source of Name
This entry was named for Thabit ibn Qurra.
Sources
- Weisstein, Eric W. "Thâbit ibn Kurrah Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThabitibnKurrahPrime.html