OrPrimes

OrPrimes is a term used in number theory to describe a specific type of prime number. A prime number p is considered an OrPrime if it can be expressed as the sum of two prime numbers, where one of those primes is 2. In other words, an OrPrime p must satisfy the condition p = 2 + q, where both p and q are prime numbers.

This definition leads to a very simple characterization of OrPrimes. Since 2 is the only even prime number, and the sum of an even number (2) and another prime number (q) must be odd (unless q is also 2, in which case the sum is 4, which is not prime), all OrPrimes must be odd prime numbers. Therefore, an OrPrime is an odd prime number that can be represented as 2 plus another prime.

The first few OrPrimes can be found by examining prime numbers and checking if they fit the definition. For example, 5 is prime. Is 5 = 2 + q for some prime q? Yes, 5 = 2 + 3, and 3 is prime. So, 5 is an OrPrime. The next odd prime is 7. Is 7 = 2 + q for some prime q? Yes, 7 = 2 + 5, and 5 is prime. So, 7 is an OrPrime. The odd prime 11 is not an OrPrime because 11 - 2 = 9, and 9 is not prime. The sequence of OrPrimes begins with 5, 7, 13, 19, 31, and so on. The existence of OrPrimes is closely related to Goldbach's conjecture, which states that every even integer greater than 2 is the sum of two primes.