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The first 1000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. 1 is neither prime nor composite. The first 1000 prime numbers [ edit ]
The tables contain the prime factorization of the natural numbers from 1 to 1000. When n is a prime number, the prime factorization is just n itself, written in bold below. The number 1 is called a unit. It has no prime factors and is neither prime nor composite.
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...
Mersenne primes and perfect numbers are two deeply interlinked types of natural numbers in number theory. Mersenne primes, named after the friar Marin Mersenne, are prime numbers that can be expressed as 2p − 1 for some positive integer p. For example, 3 is a Mersenne prime as it is a prime number and is expressible as 22 − 1.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
However, it does not contain all the prime numbers, since the terms gcd(n + 1, a n) are always odd and so never equal to 2. 587 is the smallest prime (other than 2) not appearing in the first 10,000 outcomes that are different from 1. Nevertheless, in the same paper it was conjectured to contain all odd primes, even though it is rather inefficient.
The only primes below 1000 with weak irregular index 3 are 307, 311, 353, 379, 577, 587, 617, 619, 647, 691, 751, and 929. Besides, 491 is the only prime below 1000 with weak irregular index 4, and all other odd primes below 1000 with weak irregular index 0, 1, or 2.
The largest known prime number is 2 82,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018. A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer.