71 (number)
| ||||
|---|---|---|---|---|
| Cardinal | seventy-one | |||
| Ordinal | 71st (seventy-first) | |||
| Factorization | prime | |||
| Prime | 20th | |||
| Divisors | 1, 71 | |||
| Greek numeral | ΟΑ´ | |||
| Roman numeral | LXXI, lxxi | |||
| Binary | 10001112 | |||
| Ternary | 21223 | |||
| Senary | 1556 | |||
| Octal | 1078 | |||
| Duodecimal | 5B12 | |||
| Hexadecimal | 4716 | |||
71 (seventy-one) is the natural number following 70 and preceding 72.
In mathematics
[edit]71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime.[1][2]
71 is a centered heptagonal number.[3]
It is a regular prime[4], a Ramanujan prime[5], a Higgs prime[6], and a good prime[7].
It is a Pillai prime, since is divisible by 71, but 71 is not one more than a multiple of 9.[8] It is part of the last known pair (71, 7) of Brown numbers, since .[9]
71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also, Heegner numbers).[10]
71 is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.[11][12]
See also
[edit]References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A006567 (Emirps (primes whose reversal is a different prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Baker, Alan (January 2017). "Mathematical spandrels". Australasian Journal of Philosophy. 95 (4): 779–793. doi:10.1080/00048402.2016.1262881. S2CID 218623812.
- ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A007703 : Regular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "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". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A007459 : a(n+1) = smallest prime > a(n) such that a(n+1)-1 divides the product (a(1)...a(n))^2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A028388 : prime(n) such that prime(n)^2 > prime(n-i)*prime(n+i) for all 1 <= i <= n-1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A063980 (Pillai primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Berndt, Bruce C.; Galway, William F. (2000). "On the Brocard–Ramanujan Diophantine equation ". Ramanujan Journal. 4 (1): 41–42. doi:10.1023/A:1009873805276. MR 1754629. S2CID 119711158.
- ^ Sloane, N. J. A. (ed.). "Sequence A046004 (Discriminants of imaginary quadratic fields with class number 7 (negated).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-08-03.
- ^ Sloane, N. J. A. (ed.). "Sequence A002267 (The 15 supersingular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Duncan, John F. R.; Ono, Ken (2016). "The Jack Daniels problem". Journal of Number Theory. 161: 230–239. doi:10.1016/j.jnt.2015.06.001. MR 3435726. S2CID 117748466.
 | This article about a number is a stub. You can help Wikipedia by expanding it. |