# 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 [7], or [1], pp. 430—431, and [4]). The number of irregulär primes is known to be infinite; a short proof for this, due to Carlitz [2], can be found in [1], pp. 381—382. Jensen [3] proved in 1915 that there exist infinitely many irregulär primes l (mod 4). Montgomery [6] 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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## References

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NOTE ON IRREGULAR PRIMES
where Bm denotes a Bernoulli number in the even-suffix notation. Jensen has proved that there exist infinitely many irregular primes of the form 4n+3 (for the proof see [3, p. 82]; see also [4]). In
PROOF OF FERMAT'S LAST THEOREM FOR ALL PRIME EXPONENTS LESS THAN 4002.
• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1955
* Based on research supported in part under Contract N6ori-02053, monitored by the Office of Naval Research. ' Harish-Chandra, "Plancherel Formula for the 2 X 2 Real Unimodular Group," these