Natural number
57 (fifty-seven ) is thenatural number following56 and preceding58 . It is acomposite number .
57 is asemiprime ,[ 1] Blum integer ,[ 2] Leyland number .[ 3]
The splitLie algebra E7+ 1 / 2 has a 57-dimensionalHeisenberg algebra as itsnilradical , and the smallest possiblehomogeneous space forE8 is also 57-dimensional.[ 4]
Although fifty-seven is not prime, it is jokingly known as theGrothendieck prime after a legend in which the mathematicianAlexander Grothendieck gave it as an example of a prime number, not realizing it was divisible by three and nineteen.[ 5] Hermann Weyl , in a published article.[ 6]
^ Sloane, N. J. A. (ed.)."Sequence A001358 (Semiprimes (or biprimes): products of two primes)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A016105 (Blum integers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A076980 (Leyland numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Vogan, David (2007),"The character table for E8 " (PDF) ,Notices of the American Mathematical Society ,54 (9):1122– 1134,MR 2349532 ^ Jackson, Allyn (2004b)."Comme Appelé du Néant—As if Summoned from the Void: The Life of Alexandre Grothendieck" (PDF) .Notices of the American Mathematical Society 51 (10). Providence, RI:American Mathematical Society : 1196, 1197.MR 2104915 .Zbl 1168.01339 . ^ Weyl, Hermann (1951). "A Half-Century of Mathematics".American Mathematical Monthly 58 (5). Washington, D.C.:Mathematical Association of America : 532.doi :10.1080/00029890.1951.11999734 .JSTOR 2306319 .S2CID 126101329 .An old conjecture of Goldbach's maintains that there even come along again and again pairs of primes of the smallest possible difference 2, like 57 and 59.
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