Classes of prime numbers

Proth prime

A Proth number is a natural number N of the form where k and n are positive integers, k is odd and . A Proth prime is a Proth number that is prime. They are named after the French mathematician François Proth. The first few Proth primes are 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857 (OEIS: ). It is still an open question whether an infinite number of Proth primes exist. It was shown in 2022 that the reciprocal sum of Proth primes converges to a real number near 0.747392479, substantially less than the value of 1.093322456 for the reciprocal sum of Proth numbers. The primality of Proth numbers can be tested more easily than many other numbers of similar magnitude. (Wikipedia).

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prob6

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PrimeGrid | Binary number | False positives and false negatives | Goldbach's weak conjecture | Probable prime | Deterministic algorithm | Conjecture | Las Vegas algorithm | Proth's theorem | Diffie–Hellman problem | Composite number | Seventeen or Bust | Natural number | Integer | Mersenne prime | Discrete logarithm | Thabit number | Fermat number | Prime number | Parity (mathematics) | Cullen number