Euler's "lucky" numbers are positive integers n such that for all integers k with 1 ≤ k < n, the polynomial k2 − k + n produces a prime number. When k...

In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1 cosh ⁡ t = 2 e...

(3-manifold topology) – see Seifert fiber space Lucky numbers of Euler Euler's constant gamma (γ), also known as the Euler–Mascheroni constant Eulerian integers...

many lucky primes. Lucky numbers of Euler Fortunate number Happy number Harshad number Josephus problem Gambling Lottery Keno Weisstein, Eric W. "Lucky Number"...

element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted...

a Carmichael number. Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas...

2 {\displaystyle p=2} . The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author and senior...

the sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be...

prime numbers, then 2n × p × q and 2n × r are a pair of amicable numbers. Thābit ibn Qurra's theorem corresponds to the case m = n − 1. Euler's rule creates...

exist absolute Euler pseudoprimes, numbers which are Euler pseudoprimes to every base relatively prime to themselves. The absolute Euler pseudoprimes are...

factor of n. The motivation for this definition is the fact that all prime numbers n satisfy the above equation, as explained in the Euler's criterion...

2013 Lucky numbers of Euler, producing prime-generating polynomials A number believed to affect one's luck Lucky number combinations, an element of Chinese...

Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The nth triangular number is the number of dots in...

the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative...

composite numbers are exactly the numbers that are not prime and not a unit. E.g., the integer 14 is a composite number because it is the product of the two...

the OEIS). Palindromic numbers receive most attention in the realm of recreational mathematics. A typical problem asks for numbers that possess a certain...

a composite natural number with an even number of digits, that can be factored into two natural numbers each with half as many digits as the original number...

Riemann zeta function. According to Euler, Goldbach showed (in a now-lost letter) that the sum of ⁠1/p − 1⁠ over the set of perfect powers p, excluding 1 and...

of the Trojan War, who was also powerful but imperfect. Strong Achilles numbers are Achilles numbers whose Euler totients are also Achilles numbers;...

magnitude and orders of magnitude (numbers) for named powers of ten. There are two conventions for naming positive powers of ten, beginning with 109, called...

(1999) [1920]. History of the Theory of Numbers. Vol. 2. Providence: American Mathematical Society. p. 16. ISBN 978-0-8218-1935-7. Euler, Leonhard (1813)....

and 5, using 3 & 4 (34 - 43). 17 is a Fermat prime. 17 is one of six lucky numbers of Euler. Since seventeen is a Fermat prime, regular heptadecagons can...

of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem. Later, it became a significant topic for Euler,...

{\displaystyle p=2,3,5,11{\text{ and }}17} (the lucky numbers of Euler), corresponding to other Heegner numbers. Given a positive integer S, there may be infinitely...

as eγn log(log(n)), where γ is the Euler–Mascheroni constant. Hence colossally abundant numbers capture the notion of having many divisors by requiring...

Smooth numbers are especially important in cryptography, which relies on factorization of integers. 2-smooth numbers are simply the powers of 2, while...

cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle theorem). Euler conjectured that a...

to base a is always an Euler–Jacobi pseudoprime, an Euler pseudoprime and a Fermat pseudoprime to that base, but not all Euler and Fermat pseudoprimes...

numbers are prime. Indeed, the first five Fermat numbers F0, ..., F4 are easily shown to be prime. Fermat's conjecture was refuted by Leonhard Euler in...

perfect numbers, while numbers whose sum of proper factors is less than the number itself are called deficient numbers. The first known classification of numbers...