3511
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | three thousand five hundred eleven | |||
| Ordinal | 3511th (three thousand five hundred eleventh) | |||
| Factorization | prime | |||
| Prime | Yes | |||
| Divisors | 1, 3511 | |||
| Greek numeral | ,ΓΦΙΑ´ | |||
| 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". http://mathworld.wolfram.com/Emirp.html.
- ↑ The Prime Glossary: Wieferich prime, http://primes.utm.edu/glossary/xpage/WieferichPrime.html
- ↑ Beeger, N. G. W. H. (1922), "On a new case of the congruence 2p − 1 ≡ 1 (p2)", Messenger of Mathematics 51: 149–150, https://archive.org/stream/messengerofmathe5051cambuoft#page/148/mode/2up
- ↑ 4.0 4.1 Dorais, F. G.; Klyve, D. (2011). "A Wieferich Prime Search Up to 6.7×1015". Journal of Integer Sequences 14 (9). http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Klyve/klyve3.pdf. Retrieved 2011-10-23.
- ↑ Meissner, W. (1913), "Über die Teilbarkeit von 2p − 2 durch das Quadrat der Primzahl p=1093" (in de), Sitzungsber. D. Königl. Preuss. Akad. D. Wiss. (Berlin) Zweiter Halbband. Juli bis Dezember: 663–667
- ↑ "Sloane's A062786 : Centered 10-gonal numbers". OEIS Foundation. https://oeis.org/A062786.
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