3511 (number)

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3510 3511 3512
Cardinal three thousand five hundred eleven
Ordinal 3511th
(three thousand five hundred and eleventh)
Factorization 3511
Prime Yes
Divisors 1, 3511
Roman numeral MMMDXI
Binary 1101101101112
Ternary 112110013
Quaternary 3123134
Quinary 1030215
Senary 241316
Octal 66678
Duodecimal 204712
Hexadecimal DB716
Vigesimal 8FB20
Base 36 2PJ36

3511 (three thousand, five hundred and eleven) is the natural number following 3510 and preceding 3512.

3511 is a prime number, and is also an emirp: a different prime when its digits are reversed.[1]

3511 is a Wieferich prime,[2] found to be so by N. G. W. H. Beeger in 1922[3] and the largest known[4] – the only other being 1093.[5] If any other Wieferich primes exist, they must be greater than 6.7×1015.[4]

3511 is the 27th centered decagonal number.

References[edit]

  1. ^ Weisstein, Eric W., "Emirp", MathWorld.
  2. ^ The Prime Glossary: Wieferich prime 
  3. ^ Beeger, N. G. W. H. (1922), "On a new case of the congruence 2p − 1 ≡ 1 (p2)", Messenger of Mathematics 51: 149–150 Archived at WebCite
  4. ^ a b Dorais, F. G.; Klyve, D. (2011). "A Wieferich Prime Search Up to 6.7×1015". Journal of Integer Sequences 14 (9). Zbl 05977305. Retrieved 2011-10-23. 
  5. ^ Meissner, W. (1913), "Über die Teilbarkeit von 2p − 2 durch das Quadrat der Primzahl p=1093", Sitzungsber. D. Königl. Preuss. Akad. D. Wiss. (in German) (Berlin), Zweiter Halbband. Juli bis Dezember: 663–667