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.htmlOnLine Encyclopedia of Integer Sequences, http://www.research.att.com/cgibin/access.cgi/as/njas/sequences/eisA.c gi?Anum=A000928 sequence 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^{}:
$p$ Class Number 3 1 5 1 7 1 11 1 13 1 17 1 19 1 23 3 29 8 31 9 37 37 41 121 43 211 47 695 53 4889 59 41241 61 76301 An excellent reference for this is [1].
Remarks:

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Notice that $37$ divides $37$, and $59$ divides $41241=3\cdot 59\cdot 233$, thus $37,\mathrm{\hspace{0.25em}59}$ are irregular primes (see above).

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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.

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References
 1 L. C. Washington, Introduction to Cyclotomic Fields, SpringerVerlag, New York.
Title  examples of regular primes 

Canonical name  ExamplesOfRegularPrimes 
Date of creation  20130322 14:05:58 
Last modified on  20130322 14:05:58 
Owner  alozano (2414) 
Last modified by  alozano (2414) 
Numerical id  10 
Author  alozano (2414) 
Entry type  Example 
Classification  msc 11R18 
Classification  msc 11R29 
Related topic  ClassNumbersAndDiscriminantsTopicsOnClassGroups 