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Reference.org
Maier's matrix method
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<p>Maier's matrix method is a technique in <a href="/facts/Analytic_number_theory/mrHbWwrx">analytic number theory</a> by <a href="/facts/Helmut_Maier/n4b29Yc8">Helmut Maier</a> that is used to demonstrate the existence of intervals of natural numbers within which the prime numbers are distributed with a certain property. In particular, it has been used to prove <a href="/facts/Maier%2527s_theorem/j4ff9yop">Maier's theorem</a> (Maier 1985) and also the existence of chains of large gaps between consecutive primes (Maier 1981). The method uses estimates for the distribution of prime numbers in arithmetic progressions to prove the existence of a large set of intervals where the number of primes in the set is well understood and hence that at least one of the intervals contains primes in the required distribution. </p>