Abstract
By a sieve method and the use of a computer, a search for primes, forming arithmetic series, is reported. The longest series found contained 13 primes.
If the local prime density in an interval is unusually large, we say that there is a cluster of primes in the interval. Clusters of large primes are searched for by looking for repetitions of patterns of primes chosen from the beginning of the prime series. The densest large cluster found is 429 983 158 710+11, 13, 17, 19, 23, 37, 41, 43, 47, 53, and 59, with 11 primes out of 49 numbers. The average prime density this high up in the number series is one number only in about 27.
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Riesel, H. Primes forming arithmetic series and clusters of large primes. BIT 10, 333–342 (1970). https://doi.org/10.1007/BF01934202
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DOI: https://doi.org/10.1007/BF01934202