| ||||
---|---|---|---|---|
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 | |||
Senary | 241316 | |||
Octal | 66678 | |||
Duodecimal | 204712 | |||
Hexadecimal | DB716 |
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]
In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1. Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's Last Theorem, at which time both of Fermat's theorems were already well known to mathematicians.
In number theory, a Wilson prime is a prime number such that divides , where "" denotes the factorial function; compare this with Wilson's theorem, which states that every prime divides . Both are named for 18th-century English mathematician John Wilson; in 1770, Edward Waring credited the theorem to Wilson, although it had been stated centuries earlier by Ibn al-Haytham.
In number theory, a Wall–Sun–Sun prime or Fibonacci–Wieferich prime is a certain kind of prime number which is conjectured to exist, although none are known.
79 (seventy-nine) is the natural number following 78 and preceding 80.
73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.
31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.
37 (thirty-seven) is the natural number following 36 and preceding 38.
107 is the natural number following 106 and preceding 108.
1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
300 is the natural number following 299 and preceding 301.
700 is the natural number following 699 and preceding 701.
3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.
Nicolaas George Wijnand Henri Beeger was a Dutch mathematician. His 1916 doctorate was on Dirichlet series. He worked for most of his life as a teacher, working on mathematics papers in his spare evenings. After his retirement as a teacher at 65, he began corresponding with many contemporary mathematicians and dedicated himself to his work. Tilburg University still hold biennial lectures entitled the Beeger lectures in his honour.
149 is the natural number between 148 and 150.
In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if are coprime integers, then for any integer , there is a prime number p that divides and does not divide for any positive integer , with the following exceptions:
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered attention throughout history in part because distal extremities in humans typically contain five digits.
In mathematics, a Wieferich pair is a pair of prime numbers p and q that satisfy
In number theory, the Fermat quotient of an integer a with respect to an odd prime p is defined as
In algebraic number theory Eisenstein's reciprocity law is a reciprocity law that extends the law of quadratic reciprocity and the cubic reciprocity law to residues of higher powers. It is one of the earliest and simplest of the higher reciprocity laws, and is a consequence of several later and stronger reciprocity laws such as the Artin reciprocity law. It was introduced by Eisenstein (1850), though Jacobi had previously announced a similar result for the special cases of 5th, 8th and 12th powers in 1839.