3511

← 3510 3511 3512 →
Cardinalthree thousand five hundred eleven
Ordinal3511th
(three thousand five hundred eleventh)
Factorizationprime
PrimeYes
Divisors1, 3511
Greek numeral,ΓΦΙΑ´
Roman numeralMMMDXI, mmmdxi
Binary1101101101112
Ternary112110013
Senary241316
Octal66678
Duodecimal204712
HexadecimalDB716

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.[6]

References

  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 from the original on 2012-11-11
  4. ^ a b Dorais, F. G.; Klyve, D. (2011). "A Wieferich Prime Search Up to 6.7×1015" (PDF). Journal of Integer Sequences. 14 (9). Zbl 1278.11003. 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), Zweiter Halbband. Juli bis Dezember, Berlin: 663–667
  6. ^ "Sloane's A062786 : Centered 10-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-03.


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