Prime numbers properties II

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The actual sole property of prime numbers is by definition they have one  and unique divisor else than themselves ;-) However this group hosts  cody problems about some  formulas related to some prime  numbers. I wish all of you to simultaneously enjoy solving my problems, learn some new interesting notions in number theory, and Matlab coding tricks. I welcome your  feedbacks and remarks for me to improve. Please do not hesitate to return me an error if you find one. Check my other group Prime numbers properties I for some more cody problem in number theory / prime numbers.

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Problem Title	Likes	Solvers
Problem 60967. List primes which are the sum of two consecutive lower primes plus minus one Created by: Nicolas Douillet Tags math, primes, integers	2	71
Problem 60965. List the near-square primes, p = n² + 1 (Landau's 4th problem) Created by: Nicolas Douillet Tags math, square, primes	3	66
Problem 60953. Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set Created by: Nicolas Douillet Tags math, primes, distance	4	42
Problem 60969. Check p = 4n +/- 1, the generic formula for odd prime numbers Created by: Nicolas Douillet Tags math, primes, integers	3	49
Problem 60970. Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3 Created by: Nicolas Douillet Tags math, primes, integers	2	44
Problem 60972. Check Bertrand-Chebyshev's theorem about prime numbers Created by: Nicolas Douillet Tags math, primes, integers	2	42
Problem 60971. List the twin prime couples Created by: Nicolas Douillet Tags math, primes, integers	2	41
Problem 60975. Check Legendre's conjecture Created by: Nicolas Douillet Tags math, square, primes	2	44
Problem 60976. List the complementary / symetric prime couples Created by: Nicolas Douillet Tags math, primes, integers	3	39
Problem 60977. Linear primes p' = mp + n Created by: Nicolas Douillet Tags math, primes, integers	3	38