71 (number)

Quality 0.50 · 4 views · Updated 2 months ago

title: "71 (number)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["integers"] topic_path: "general/integers" source: "https://en.wikipedia.org/wiki/71_(number)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::data[format=table title="Infobox number"]

FieldValue
number71
factorizationprime
prime20th
divisor1, 71
::

| number = 71 | factorization = prime | prime = 20th | divisor = 1, 71 71 (seventy-one) is the natural number following 70 and preceding 72.

TOC

In mathematics

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.{{cite journal | last = Baker | first = Alan | author-link = Alan Baker (philosopher) | date = January 2017 | doi = 10.1080/00048402.2016.1262881 | issue = 4 | journal = Australasian Journal of Philosophy | pages = 779–793 | title = Mathematical spandrels | volume = 95| s2cid = 218623812 }}

71 is a centered heptagonal number.

It is a regular prime, a Ramanujan prime, a Higgs prime, and a good prime.

It is a Pillai prime, since 9!+1 is divisible by 71, but 71 is not one more than a multiple of 9. It is part of the last known pair (71, 7) of Brown numbers, since 71^{2}=7!+1.{{cite journal | last1 = Berndt | first1 = Bruce C. | last2 = Galway | first2 = William F. | doi = 10.1023/A:1009873805276 | issue = 1 | journal = Ramanujan Journal | mr = 1754629 | pages = 41–42 | title = On the Brocard–Ramanujan Diophantine equation n!+1=m^2 | volume = 4 | year = 2000| s2cid = 119711158

71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also Heegner numbers).

71 is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.{{cite journal | last1 = Duncan | first1 = John F. R. | last2 = Ono | first2 = Ken | author2-link = Ken Ono | doi = 10.1016/j.jnt.2015.06.001 | journal = Journal of Number Theory | mr = 3435726 | pages = 230–239 | title = The Jack Daniels problem | volume = 161 | year = 2016| s2cid = 117748466 | doi-access = free | arxiv = 1411.5354

References

References

  1. {{cite OEIS. A006567. Emirps (primes whose reversal is a different prime)
  2. {{Cite OEIS. A069099. Centered heptagonal numbers
  3. "Sloane's A007703 : Regular primes". OEIS Foundation.
  4. "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.
  5. "Sloane's A007459 : a(n+1) = smallest prime > a(n) such that a(n+1)-1 divides the product (a(1)...a(n))^2". OEIS Foundation.
  6. "Sloane's A028388 : prime(n) such that prime(n)^2 > prime(n-i)*prime(n+i) for all 1 <= i <= n-1". OEIS Foundation.
  7. {{Cite OEIS. A063980. Pillai primes
  8. {{Cite OEIS. A046004. Discriminants of imaginary quadratic fields with class number 7 (negated).
  9. {{Cite OEIS. A002267. The 15 supersingular primes

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::

integers