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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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