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Below are listed the first prime numbers of many named forms and types. More details are in the article for the name. n is a natural number (including 0) in the definitions. Balanced primes. Primes with equal-sized prime gaps after and before them, so that they are equal to the arithmetic mean of the nearest primes after and before.
The timestamp can be shifted by any time shift value. Directly after the timestamp follows the version nibble, that must have a value of 7. The variant bits have to be 10x. Remaining 74 bits are random seeded counter (optional, at least 12 bits but no longer than 42 bits) and random. Two counter rollover handling methods can be used together:
Self-descriptive number. In mathematics, a self-descriptive number is an integer m that in a given base b is b digits long in which each digit d at position n (the most significant digit being at position 0 and the least significant at position b −1) counts how many instances of digit n are in m .
As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction 5 / 7 when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2, respectively).
Other than M 0 = 0 and M 1 = 1, all other Mersenne numbers are also congruent to 3 (mod 4). Consequently, in the prime factorization of a Mersenne number ( ≥ M 2 ) there must be at least one prime factor congruent to 3 (mod 4). A basic theorem about Mersenne numbers states that if M p is prime, then the exponent p must also be prime.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. [1] [2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a ...
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 ...