In Theory of the numbers, the second conjecture of Hardy-Littlewood relates to the number of prime numbers.
Either π ( X ) the number of prime numbers p such as p ≤ X , the conjecture postulates that
π ( X + there ) - π ( X ) ≤ π ( there )
for all X , there ≥ 2.
What means that the number of prime numbers between X + 1 and X + is there always lower or equal to the number of prime numbers between 1 and there . This is probably false in general and incompatible with the first conjecture of Hardy-Littlewood as showed it Richards in a nonobvious way in 1974. It is probable that the conjecture will be cancelled for very great values of X and there .
there would not be a problem with this formulation. If one poses X = there, that gives:
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