641

Number
$641$ (six hundred and forty-one) is:


 * The $116$th prime number


 * The $1$st of the $29$th pair of twin primes:
 * $643 - 641 = 2$


 * The larger of the $10$th pair of primes whose prime gap is $10$:
 * $641 - 631 = 10$


 * The $14$th Proth prime after $3$, $5$, $13$, $17$, $41$, $97$, $113$, $193$, $241$, $257$, $353$, $449$, $577$:
 * $641 = 10 \times 2^6 + 1$


 * The $28$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $\ldots$, $233$, $239$, $251$, $281$, $293$, $359$, $419$, $431$, $443$, $491$, $509$, $593$:
 * $2 \times 641 + 1 = 1283$, which is prime.


 * One of the two prime factors of the $5$th Fermat number $2^{\paren {2^5} } + 1$, the other being $6 \, 700 \, 417$:
 * $641 = 5 \times 2^7 + 1$

Also see