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A note on the least prime in an arithmetic progression with a prime difference. (English) Zbl 0215.35302
Let \(P(k,l)\) denote the least prime \(\equiv l\pmod k\) where \((k,l)=1\). Then it is shown that for any given \(l\) there exist infinitely many primes \(q\) for which
\[ P(q,l)<c(\varepsilon)q^{\theta+\varepsilon} \]
where \(\theta=2e^{1/4}(2e^{1/4}-1)^{-1}\).

MSC:
11N13 Primes in congruence classes
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