In Mathematics
Forty-one is the 13th smallest prime number. The next is forty-three, with which it comprises a twin prime. It is also the sum of the first six prime numbers (2 + 3 + 5 + 7 + 11 + 13), and the sum of three primes (11 + 13 + 17).
Forty-one is also the 12th supersingular prime, a Sophie Germain prime and a Newman–Shanks–Williams prime. 41 is the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, {41, 83, 167}. It is an Eisenstein prime, with no imaginary part and real part of the form 3n − 1. 41 is a Proth prime as it is 5 × 23 + 1.
The number figures in the polynomial f(n) = n2 + n + 41, which yields primes for −40 ≤ n < 40. This is also called the lucky number of Euler Prime. It is the biggest of such primes.
Forty-one is the sum of two squares, 42 + 52. Adding up the sums of divisors for 1 through 7 yields 41.
41 is the smallest integer whose reciprocal has a 5-digit repetend. That is a consequence of the fact that 41 is a factor of 99999.
It is a centered square number.
Read more about this topic: 41 (number)
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