# 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 $\mathsf{Pr} \infty \mathsf{fWiki}$.

## 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. http://mathworld.wolfram.com/ThabitibnKurrahPrime.html