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Brocard's Conjecture

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BrocardsConjecture

Brocard's conjecture states that

pi(p_(n+1)^2)-pi(p_n^2)>=4

for n>=2, where pi(n) is the prime counting function and p_n is the nth prime. For n=1, 2, ..., the first few values are 2, 5, 6, 15, 9, 22, 11, 27, 47, 16, ... (OEIS A050216).

See also

Andrica's Conjecture, Cramér Conjecture

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References

Sloane, N. J. A. Sequence A050216 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Brocard's Conjecture

Cite this as:

Weisstein, Eric W. "Brocard's Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrocardsConjecture.html

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