41 (forty-one) is the natural number following 40 and preceding 42.
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- the 13th smallest prime number. The next is 43, making both twin primes.
- the sum of the first six prime numbers (2 + 3 + 5 + 7 + 11 + 13).
- the 12th supersingular prime[1]
- a Newman–Shanks–Williams prime.[2]
- the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, {41, 83, 167}.
- an Eisenstein prime, with no imaginary part and real part of the form 3n − 1.
- a Proth prime as it is 5 × 23 + 1.[3]
- the largest lucky number of Euler: the polynomial f(k) = k2 − k + 41 yields primes for all the integers k with 1 ≤ k < 41.
- the sum of two squares (42 + 52), which makes it a centered square number.[4]
- the sum of the first three Mersenne primes, 3, 7, 31.[5]
- the sum of the sum of the divisors of the first 7 positive integers.
- the smallest integer whose reciprocal has a 5-digit repetend. That is a consequence of the fact that 41 is a factor of 99999.
- the smallest integer whose square root has a continued fraction with period 3.[6]
- a prime index prime, as 13 is prime.
Kellogg, William O. (2010). Barron's AP United States History (9th ed.). Barron's Educational Series. p. 364. ISBN 9780764141843. George H. W. Bush (Republican) [Bush 41—i.e., the first President Bush, George H. W. Bush was the forty-first President of the United States, and so some have referred to him in this way since the election of his son, George W. Bush or Bush 43—the forty-third president of the United States.]