## Blaise Pascal was born on this day 394 years ago.

### Properties of the number 641:

641 is a cyclic number.641 and 643 form a twin prime pair.

641 has 7 antidivisors and 640 totatives.

641 has a prime digit sum 11 in base 10.

641 has sum of divisors equal to 642 which is a sphenic number.

Reversing the decimal digits of 641 results in a semiprime.

641 = 321

^{2}- 320

^{2}is the difference of 2 nonnegative squares in 1 way.

641 is the difference of 2 positive pentagonal numbers in 1 way.

641 = 4

^{2}+ 25

^{2}is the sum of 2 positive squares in 1 way.

641 = 6

^{2}+ 11

^{2}+ 22

^{2}is the sum of 3 positive squares.

641

^{2}= 200

^{2}+ 609

^{2}is the sum of 2 positive squares in 1 way.

641

^{2}is the sum of 3 positive squares.

641 is a proper divisor of 487

^{4}- 1.

641 is an emirp in (at least) the following bases: 3, 9, 11, 13, 15, 22, 27, 29, 36, 37, 45, 47, 48, 53, 54, 57, 59, 61, 71, 75, 77, 79, 82, 83, 85, 86, 87, 88, 89, and 90.

641 is palindromic in (at least) the following bases: 20, -12, -13, -32, -40, -64, and -80.

641 in base 11 = 533 and consists of only the digits '3' and '5'.

641 in base 12 = 455 and consists of only the digits '4' and '5'.

641 in base 14 = 33b and consists of only the digits '3' and 'b'.

641 in base 19 = 1ee and consists of only the digits '1' and 'e'.

641 in base 20 = 1c1 and consists of only the digits '1' and 'c'.

### The number 641 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A001097: Twin primes.

A001359: Lesser of twin primes.

A005384: Sophie Germain primes p: 2p+1 is also prime.

A005846: Primes of the form n^2 + n + 41.

A007519: Primes of form 8n+1, that is, primes congruent to 1 mod 8.

A023201: Sexy primes: numbers n such that n and n + 6 are both prime.

A104272: Ramanujan primes R_n: a(n) is the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x.

A106856: Primes of the form x^2+xy+2y^2, with x and y nonnegative.

A212959: Number of (w,x,y) such that w,x,y are all in {0,...,n} and |w-x| = |x-y|.

A235266: Primes whose base 2 representation is also the base 3 representation of a prime.

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