Divergence of the Sum of the Reciprocals of Prime Numbers and the Second Mertens Theorem

[LucasMalaizier]

• Definition of the sequence of prime numbers, prime_seq
• Proof of its growth and correctness
• Proof of the divergence of the sum of the reciprocals of prime numbers
• Proof of the discrete and continuous Abel transformations
• Proof of a comparison relation for the first Chebyshev function
• Incomplete proof of the second Mertens theorem (assuming the first as given)