41 (number)

In mathematics

41 is:

• 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).
• a regular prime.
• a Ramanujan prime.
• a harmonic prime.
• a good prime.
• the 12th supersingular prime.
• a Newman–Shanks–Williams prime.
• 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.
• the largest lucky number of Euler: the polynomial yields primes for all the integers k with {{nowrap|1 ≤ k
• the sum of two consecutive squares (42 + 52), which makes it a centered square number.
• the sum of the first three Mersenne primes, 3, 7, 31.
• 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 simple continued fraction with period 3.
• a prime index prime, as 13 is prime.

In other fields

• In Mexico "cuarenta y uno" (41) is slang referring to a homosexual. This is due to the 1901 arrest of 41 homosexuals at a hotel in Mexico City during the government of Porfirio Díaz (1876–1911). See: Dance of the Forty-One.
• An international calling code for Switzerland.

References

References

1. "Sloane's A007703 : Regular primes". OEIS Foundation.
2. "Sloane's A104272 : 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". OEIS Foundation.
3. "Sloane's A092101 : Harmonic primes". OEIS Foundation.
4. "Sloane's A028388 : prime(n) such that prime(n)^2 > prime(n-i)*prime(n+i) for all 1 <= i <= n-1". OEIS Foundation.
5. "Sloane's A002267 : The 15 supersingular primes". OEIS Foundation.
6. "Sloane's A088165 : NSW primes". OEIS Foundation.
7. "Sloane's A080076 : Proth primes". OEIS Foundation.
8. {{Cite OEIS. A001844. Centered square numbers: a(n) is 2n(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z equal to Y+1) ordered by increasing Z; then sequence gives Z values.
9. {{Cite OEIS. A000668. Mersenne primes (primes of the form 2^n - 1).
10. "Sloane's A013646: Least ''m'' such that continued fraction for sqrt(''m'') has period ''n''.". OEIS Foundation.
11. "Reference 1".
12. "Reference 2".