Let  be a prime with  digits and let  be a constant. Call  an "-prime" if the concatenation of the first  digits of  (ignoring the decimal point if one is present) give . Constant primes are therefore a special type of integer sequence primes, with e-primes, pi-primes, and phi-primes being perhaps the most prominent examples.

The following table summarizes the indices of known constant primes for some named mathematical constants.

constant	name of primes		OEIS	giving prime
Apéry's constant			A119334	10, 55, 109, 141
Catalan's constant			A118328	52, 276, 25477
Champernowne constant			A071620	10, 14, 24, 235, 2804, 4347, 37735, 68433
Copeland-Erdős constant			A227530	1, 2, 4, 11, 353, 355, 499, 1171, 1543, 5719, 11048
e	e-prime		A064118	1, 3, 7, 85, 1781, 2780, 112280, 155025
Euler-Mascheroni constant			A065815	1, 3, 40, 185, 1038, 22610, 179849
Glaisher-Kinkelin constant			A118420	7, 10, 18, 64, 71, 527, 1992, 5644, 8813, 19692
Golomb-Dickman constant			A174974	6, 27, 57, 60, 1659, 2508
golden ratio	phi-prime		A064119	7, 13, 255, 280, 97241
Khinchin's constant			A118327	1, 407, 878, 4443, 4981, 6551, 13386, 28433
natural logarithm of 2			A228226	321, 466, 1271, 15690, 18872, 89973
natural logarithm of 10			A228240	1, 2, 40, 242, 842, 1541, 75067
pi	pi-prime		A060421	2, 6, 38, 16208, 47577, 78073, 613373
Pythagoras's constant			A115377	55, 97, 225, 11260, 11540
Soldner's constant			A122422	4, 144, 227, 444, 19474
Theodorus's constant			A119344	2, 3, 19, 111, 116, 641, 5411, 170657

The following table summarizes discoverers and discovery dates for some large constant primes.

The following table summarizes the values of known constant primes for some named mathematical constants. The first of the -primes (where  is Pythagoras's constant) was found by J. Earls (Pickover 2002, p. 334) and, contrary to Pickover's claim, is actually the smallest (rather than the largest known) example.

constant		OEIS	primes
Apéry's constant		A119333	1202056903, 1202056903159594285399738161511449990764986292340498881, ...
Champernowne constant		A176942	1234567891, 12345678910111, 123456789101112131415161, ...
Catalan's constant		A118329	9159655941772190150546035149323841107741493742816721, ...
Copeland-Erdős constant		A227529	2, 23, 2357, 23571113171, ...,
e		A007512	2, 271, 2718281, ...
Euler-Mascheroni constant		A072952	5, 577, 5772156649015328606065120900824024310421, ...
Glaisher-Kinkelin constant		A118419	1282427, 1282427129, 128242712910062263, ...
Golomb-Dickman constant		A174975	624329, 624329988543550870992936383, ...
golden ratio		A064117	1618033, 1618033988749, ...
natural logarithm of 10		A228241	2, 23, 2302585092994045684017991454684364207601, ...
pi		A005042	3, 31, 314159, 31415926535897932384626433832795028841, ...
Pythagoras's constant		A115453	1414213562373095048801688724209698078569671875376948073, ...
Soldner's constant		A122422	1451, ...
Theodorus's constant		A119343	17, 173, 1732050807568877293, ...

REFERENCES:

Pickover, C. A. The Mathematics of Oz: Mental Gymnastics from Beyond the Edge. New York: Cambridge University Press, 2002.

Sloane, N. J. A. Sequences A005042, A007512, A060421, A064117, A064118, A064119, A065815, A071620, A072952, A115377, A115453, A118327, A118328, A118329, A118419, A118420, A119333, A119334, A119343, A119344, A122421, A122422, A174974, A174975, A176942, A227529, A227530, A228226, A228240, and A228241 in "The On-Line Encyclopedia of Integer Sequences."