Abstract
CERTAIN quadratic series abound in prime numbers1. Take, for example, the following Sequence in which the consecutive differences are 2, 4, 6, 8, etc. 
These are all prime numbers; the next term in this series is no longer a prime but equal to the square of the first term. The longest series of this kind known at present consists of forty prime numbers. It begins with 41, 43, 47, 53 … and ends with … 1373, 1447,1523,1601, a truly extraordinary sequence. The series starting 101, 103, 170 contains sixty-eight primes and thirty-two non-primes.
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References
Hardy, G. H., and Wright, E. M., An Introduction to the Theory of Numbers (fourth edition), 18 (Oxford, 1960).
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GOUDSMIT, S. Unusual Prime Number Sequences. Nature 214, 1164 (1967). https://doi.org/10.1038/2141164b0
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DOI: https://doi.org/10.1038/2141164b0
