3511 (number)
| ||||
---|---|---|---|---|
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.[6]
References
- ↑ Weisstein, Eric W. "Emirp". MathWorld.
- ↑ The Prime Glossary: Wieferich prime
- ↑ 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 2011-06-29
- 1 2 Dorais, F. G.; Klyve, D. (2011). "A Wieferich Prime Search Up to 6.7×1015" (PDF). Journal of Integer Sequences. 14 (9). Zbl 05977305. Retrieved 2011-10-23.
- ↑ 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
- ↑ "Sloane's A062786 : Centered 10-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-03.
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