641

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Number

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

The $116$th prime number

The smaller of the two prime factors of the $5$th Fermat number $2^{\paren {2^5} } + 1$, the other being $6 \, 700 \, 417$:

$641 = 5 \times 2^7 + 1$

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.

The smaller of the $29$th pair of twin primes:

$643 - 641 = 2$

Also see

• Next: Prime Decomposition of 5th Fermat Number

• Previous  ... Next: Proth Prime

• Previous  ... Next: Sophie Germain Prime

• Previous  ... Next: Twin Primes

• Previous  ... Next: Prime Number
• Previous  ... Next: Prime Gaps of 10

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $257$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $641$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $641$