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This is a list of articles about prime 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 are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes.
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
Printable version; In other projects ... The table below lists the largest currently known prime numbers and probable primes ... 130 146561×2 11280802-1 [50] 16 ...
Therefore, every prime number other than 2 is an odd number, and is called an odd prime. [10] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in ...
129 is the sum of the first ten prime numbers.It is the smallest number that can be expressed as a sum of three squares in four different ways: + +, + +, + +, and + +. 129 is the product of only two primes, 3 and 43, making 129 a semiprime.
1, 2, 6, 6, 30, 30, 210, 210, 210, 210, 2310, 2310. We see that for composite n every term n# simply duplicates the preceding term (n − 1)#, as given in the definition. In the above example we have 12# = p 5 # = 11# since 12 is a composite number. Primorials are related to the first Chebyshev function, written ϑ(n) or θ(n) according to:
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In mathematics, a primorial prime is a prime number of the form p n # ± 1, where p n # is the primorial of p n (i.e. the product of the first n primes). [1] Primality tests show that: p n # − 1 is prime for n = 2, 3, 5, 6, 13
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