In mathematics, Euclid numbers are integers of the form En = pn# + 1, where pn# is the nth primorial, i.e. the product of the first n prime numbers. They are named after the ancient Greek mathematician Euclid, in connection with Euclid's theorem that there are infinitely many prime numbers.
are 2, 3, 5; their product is 30, and the corresponding Euclidnumber is 31. The first few Euclid numbers are 3, 7, 31, 211, 2311, 30031, 510511, 9699691...
Euclid (/ˈjuːklɪd/; Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry"...
attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small...
algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides...
appearing as early as Euclid's Elements (VII.22) where it is called τέλειος ἀριθμός (perfect, ideal, or complete number). Euclid also proved a formation...
rational numbers, as part of the general study of number theory. The best known of these is Euclid's Elements, dating to roughly 300 BC. Of the Indian...
Euclid Beach Park was an amusement park located on the southern shore of Lake Erie in the Collinwood neighborhood of Cleveland, Ohio, which operated from...
largest known prime number is a Mersenne prime with 24,862,048 decimal digits. There are infinitely many primes, as demonstrated by Euclid around 300 BC. No...
the number 1 differently than larger numbers, sometimes even not as a number at all. Euclid, for example, defined a unit first and then a number as a...
studied in Egypt. Euclid IX 21–34 is very probably Pythagorean; it is very simple material ("odd times even is even", "if an odd number measures [= divides]...
Fibonacci numbers are important in computational run-time analysis of Euclid's algorithm to determine the greatest common divisor of two integers: the...
by = d where d is the greatest common divisor of a and b Euclid's lemma: if a prime number divides a product of two numbers, then it divides at least...
numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there...
number of partitions of 5, a value n which yields the third perfect number 496 for 2n − 1(2n − 1), by the Euclid-Euler theorem. 7 is the only number D...
world. However, the number two tree, the Washington Tree, lost its ranking in 2003 due to damage from a lightning strike, and the Euclid Tree is now considered...
rational number m/n (dividing both terms by nq). Definition 6 says that quantities that have the same ratio are proportional or in proportion. Euclid uses...
proved directly by infinite descent. Any number either is prime or is measured by some prime number. — Euclid, Elements Book VII, Proposition 32 Proposition...
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