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The primes of the form 2n+1 are the odd primes, including all primes other than 2. Some sequences have alternate names: 4 n +1 are Pythagorean primes, 4 n +3 are the integer Gaussian primes, and 6 n +5 are the Eisenstein primes (with 2 omitted).
An isolated prime (also known as single prime or non-twin prime) is a prime number p such that neither p − 2 nor p + 2 is prime. In other words, p is not part of a twin prime pair. For example, 23 is an isolated prime, since 21 and 25 are both composite. The first few isolated primes are 2, 23, 37, 47, 53, 67, 79, 83, 89, 97, ...
72 lies between the 8th pair of twin primes (71, 73), where 71 is the largest supersingular prime that is a factor of the largest sporadic group (the friendly giant), and 73 the largest indexed member of a definite quadratic integer matrix representative of all prime numbers [23] [a] that is also the number of distinct orders (without ...
Clement's congruence-based theorem characterizes the twin primes pairs of the form (, +) through the following conditions: [()! +] ((+)), +P. A. Clement's original 1949 paper [2] provides a proof of this interesting elementary number theoretic criteria for twin primality based on Wilson's theorem.
See List of prime numbers for definitions and examples of many classes of primes. Pages in category "Classes of prime numbers" The following 76 pages are in this category, out of 76 total.
Twin primes constant ... [72] 0.23571 11317 ... where the sum ranges over all primes p such that p + n is also a prime 1919 [OEIS 45] Champernowne ...
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 ...
The table below lists the largest currently known prime numbers and probable primes (PRPs) as tracked by the PrimePages and by Henri & Renaud Lifchitz's PRP Records. Numbers with more than 2,000,000 digits are shown.