# Distribution of irregular prime numbers.

```@article{Metsnkyl1976DistributionOI,
title={Distribution of irregular prime numbers.},
author={Tauno Mets{\"a}nkyl{\"a}},
journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
year={1976},
volume={1976},
pages={126 - 130}
}```
• T. Metsänkylä
• Published 1 May 1976
• Mathematics
• Journal für die reine und angewandte Mathematik (Crelles Journal)
The first few irregulär primes are 37, 59, 67, 101, 103, 131, 149 (for longer lists, see , or , pp. 430—431, and ). The number of irregulär primes is known to be infinite; a short proof for this, due to Carlitz , can be found in , pp. 381—382. Jensen  proved in 1915 that there exist infinitely many irregulär primes l (mod 4). Montgomery  generalized this by replacing 4 by any integer > 2. In this note we shall give a further generalization, by proving the following theorem.
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