examples of regular primes

Examples:

1.
These are all the irregular primes up to $1061$ :
37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, 271,
283, 293, 307, 311, 347, 353, 379, 389, 401,
409, 421, 433, 461, 463, 467, 491, 523, 541,
547, 557, 577, 587, 593, 607, 613, 617, 619,
631, 647, 653, 659, 673, 677, 683, 691, 727,
751, 757, 761, 773, 797, 809, 811, 821, 827,
839, 877, 881, 887, 929, 953, 971, 1061.
(for this, see the http://www.research.att.com/ njas/sequences/Seis.htmlOn-Line Encyclopedia of Integer Sequences, http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000928sequence A000928)
2.
The following are the first few class numbers of the cyclotomic fields $\\mathbb{Q}(\\zeta_{p})$ , where $\\zeta_{p}$ is a primitive $p$ -th root of unity:
An excellent reference for this is [1].
Remarks:
- –
  Notice that $37$ divides $37$ , and $59$ divides $41241=3\\cdot 59\\cdot 233$ , thus $37,\\ 59$ are irregular primes (see above).
- –
  The class number of the cyclotomic fields grows very quickly with $p$ . For example, $p=19$ is the last cyclotomic field of class number 1.

References

1 L. C. Washington, Introduction to Cyclotomic Fields,Springer-Verlag, New York.

单词	ExamplesOfRegularPrimes
释义	examples of regular primes Examples: 1. These are all the irregular primes up to $1061$ : 37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, 271, 283, 293, 307, 311, 347, 353, 379, 389, 401, 409, 421, 433, 461, 463, 467, 491, 523, 541, 547, 557, 577, 587, 593, 607, 613, 617, 619, 631, 647, 653, 659, 673, 677, 683, 691, 727, 751, 757, 761, 773, 797, 809, 811, 821, 827, 839, 877, 881, 887, 929, 953, 971, 1061. (for this, see the http://www.research.att.com/ njas/sequences/Seis.htmlOn-Line Encyclopedia of Integer Sequences, http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000928sequence A000928) 2. The following are the first few class numbers of the cyclotomic fields $\\mathbb{Q}(\\zeta_{p})$ , where $\\zeta_{p}$ is a primitive $p$ -th root of unity: An excellent reference for this is [1]. Remarks: – Notice that $37$ divides $37$ , and $59$ divides $41241=3\\cdot 59\\cdot 233$ , thus $37,\\ 59$ are irregular primes (see above). – The class number of the cyclotomic fields grows very quickly with $p$ . For example, $p=19$ is the last cyclotomic field of class number 1. References 1 L. C. Washington, Introduction to Cyclotomic Fields,Springer-Verlag, New York.
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