Natural number
71 (seventy-one ) is thenatural number following70 and preceding72 .
71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) areprime numbers , 71 is anemirp and more generally apermutable prime .[ 1] [ 2]
71 is acentered heptagonal number .[ 3]
It is aregular prime ,[ 4] Ramanujan prime ,[ 5] Higgs prime ,[ 6] good prime .[ 7]
It is aPillai prime , since9 ! + 1 {\displaystyle 9!+1} [ 8] Brown numbers , since71 2 = 7 ! + 1 {\displaystyle 71^{2}=7!+1} [ 9]
71 is the smallest of thirty-one discriminants of imaginaryquadratic fields with class number of 7, negated (see alsoHeegner numbers ).[ 10]
71 is the largest number which occurs as a prime factor of an order of asporadic simple group , the largest (15th)supersingular prime .[ 11] [ 12]
^ Sloane, N. J. A. (ed.)."Sequence A006567 (Emirps (primes whose reversal is a different prime))" .TheOn-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)" .TheOn-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)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Berndt, Bruce C.; Galway, William F. (2000). "On the Brocard–Ramanujan Diophantine equationn ! + 1 = m 2 {\displaystyle n!+1=m^{2}} 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).)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-08-03 .^ Sloane, N. J. A. (ed.)."Sequence A002267 (The 15 supersingular primes)" .TheOn-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.arXiv :1411.5354 doi :10.1016/j.jnt.2015.06.001 MR 3435726 .S2CID 117748466 .
400 to 999
400s, 500s, and 600s 700s, 800s, and 900s
1000s and 10,000s
1000s 10,000s
100,000s to 10,000,000,000,000s
100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000
