Irregular prime

This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.
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Definition

An irregular prime is a prime number greater than 2 that is not a regular prime. Note that 2 is neither regular nor irregular.

Occurrence

Initial examples

37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, [SHOW MORE]

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

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Facts

• Infinitude conjecture for regular primes: It is conjectured that there are infinitely many regular primes and that the density is about 0.6.