Search results
Results From The WOW.Com Content Network
A prime number is a natural number greater than 1 with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. Many of the largest known primes are Mersenne primes , numbers that are one less than a power of two, because they can utilize a specialized primality ...
All instances of log (x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln (x) or loge(x). In mathematics, the prime number theorem ( PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as ...
This conjecture is known as Lemoine's conjecture and is also called Levy's conjecture. The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, [ 32] and proved by Melfi in 1996: [ 33] every even number is a sum of two practical numbers.
Cantor's diagonal argument (among various similar names [ note 1]) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers – informally, that there are sets which in some sense contain more elements than there are positive integers.
Mersenne primes (of form 2^ p − 1 where p is a prime) In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century.
A prime gap is the difference between two successive prime numbers. The n -th prime gap, denoted gn or g ( pn) is the difference between the ( n + 1)-st and the n -th prime numbers, i.e. We have g1 = 1, g2 = g3 = 2, and g4 = 4. The sequence ( gn) of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered.
1861209×2 6789999 +1 2 December 2020 2,044,000 271 5817×2 6789459-1 9 January 2021 2,043,835 272 8435×2 6786180-1 7 January 2021 2,042,848 273 51×2 6753404 +1 26 May 2020 2,032,979 274 93×2 6750726 +1 18 September 2023 2,032,173 275 69×2 6745775 +1 21 March 2023 2,030,683 276 9995×2 6711008-1 31 December 2020 2,020,219 277 39×2 6684941 +1
Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.) This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true. For if every even number greater than 4 is the sum of two odd primes ...