A constant prime, or "
-prime," is a prime 
with 
digits equal to the concatenation
of the first 
digits of the decimal expansion
of a positive constant 
. The decimal
point and an initial 0 to its left are omitted. 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 reported indices of constant primes and probable primes for some named mathematical constants. The search limit is the reported extent of the search in decimal prefix length. A question mark indicates an unknown search limit.
| constant | name of primes |  | OEIS |  giving prime | search limit (searcher, date) |
| Apéry's constant |  | A119334 | 10, 55, 109, 141 | 9089 (E. W. Weisstein, Mar. 22, 2008) | |
| Catalan's constant |  | A118328 | 52, 276, 25477 | 166896 (E. W. Weisstein, Feb. 8, 2016) | |
| Champernowne constant |  | A071620 | 10, 14, 24, 235, 2804, 4347, 37735 | 105867 (E. W. Weisstein, Oct. 9, 2015) | |
| Copeland-Erdős constant |  | A227530 | 1, 2, 4, 11, 353, 355, 499, 1171, 1543, 5719, 11048, 68433, 97855, 292447 | 500000 (M. Rodenkirch, Jun. 18, 2016) | |
| e | e-prime |  | A064118 | 1, 3, 7, 85, 1781, 2780, 112280, 155025 | 197760 (E. W. Weisstein, Feb. 8, 2016) |
| Euler-Mascheroni constant |  | A065815 | 1, 3, 40, 185, 1038, 22610, 179849 | 206078 (E. W. Weisstein, Feb. 8, 2016) | |
| Glaisher-Kinkelin constant |  | A118420 | 7, 10, 18, 64, 71, 527, 1992, 5644, 8813, 19692 | 129009 (E. W. Weisstein, Mar. 1, 2011) | |
| Golomb-Dickman constant |  | A174974 | 6, 27, 57, 60, 1659, 2508 | 15000 (E. W. Weisstein, Jul. 25, 2013) | |
| golden ratio | phi-prime |  | A064119 | 7, 13, 255, 280, 97241 | 500000 (M. Rodenkirch, Jun. 20, 2017) |
| Khinchin's constant |  | A118327 | 1, 407, 878, 4443, 4981, 6551, 13386, 28433 | 250000 (E. W. Weisstein, Oct. 17, 2026) | |
| natural logarithm of 2 |  | A228226 | 321, 466, 1271, 15690, 18872, 89973 | 90220 (E. W. Weisstein, Oct. 28, 2015) | |
| natural logarithm of 10 |  | A228240 | 1, 2, 40, 242, 842, 1541, 75067 | 77006 (E. W. Weisstein, Oct. 12, 2015) | |
| pi | pi-prime |  | A060421 | 1, 2, 6, 38, 16208, 47577, 78073, 613373 | ? |
| Pythagoras's constant |  | A115377 | 55, 97, 225, 11260, 11540 | 187336 (E. W. Weisstein, Feb. 8, 2016) | |
| Soldner's constant |  | A122422 | 4, 144, 227, 444, 19474 | 21757 (E. W. Weisstein, Sep. 7, 2006) | |
| Theodorus's constant |  | A119344 | 2, 3, 19, 111, 116, 641, 5411, 170657 | 193924 (E. W. Weisstein, Feb. 8, 2016) |
The following table summarizes reported discoverers and discovery dates for some large constant primes and probable primes.
| constant | digits | discoverer | PrimePages |
| Champernowne constant | 37735 | E. W. Weisstein (Jul. 15, 2013) | |
| Copeland-Erdős constant | 11048 | E. W. Weisstein (Jul. 14, 2013) | |
| Copeland-Erdős constant | 68433 | E. W. Weisstein (Aug. 16, 2013) | |
| Copeland-Erdős constant | 97855 | E. W. Weisstein (Oct. 24, 2015) | |
| Copeland-Erdős constant | 292447 | M. Rodenkirch (Dec. 11, 2015) | |
| e | 112280 | E. W. Weisstein (Jul. 3, 2009) | |
| e | 155025 | E. W. Weisstein (Oct. 7, 2010) | |
| Euler-Mascheroni constant | 22610 | E. W. Weisstein (Apr. 25, 2006) | |
| Euler-Mascheroni constant | 179849 | E. W. Weisstein (Jun. 1, 2011) | |
| Glaisher-Kinkelin constant | 19692 | E. W. Weisstein (Apr. 29, 2006) | |
| Khinchin's constant | 13386 | E. W. Weisstein (Apr. 26, 2006) | |
| Khinchin's constant | 28433 | E. W. Weisstein (Apr. 27, 2006) | |
| natural logarithm of 2 | 15690 | E. W. Weisstein (Aug. 17, 2013) | |
| natural logarithm of 2 | 18872 | E. W. Weisstein (Aug. 18, 2013) | |
| natural logarithm of 2 | 89973 | E. W. Weisstein (Oct. 28, 2015) | |
| natural logarithm of 10 | 75067 | E. W. Weisstein (Oct. 10, 2015) | |
| pi | 16208 | E. T. Prothro (Dec. 13, 2001) | https://t5k.org/curios/page.php?number_id=1435 |
| pi | 47577 | E. W. Weisstein (Apr. 1, 2006) | |
| pi | 78073 | E. W. Weisstein (Jul. 13, 2006) | |
| pi | 613373 | A. Bondrescu (May 29, 2016) | |
| golden ratio | 97241 | E. W. Weisstein (Jun. 4, 2009) | |
| Pythagoras's constant | 11260 | E. W. Weisstein (Jan. 21, 2006) | https://t5k.org/curios/page.php?number_id=21191 |
| Pythagoras's constant | 11540 | E. W. Weisstein (Jan. 21, 2006) | https://t5k.org/curios/page.php?number_id=4948 |
| Theodorus's constant | 170657 | E. W. Weisstein (Aug. 18, 2013) |
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 |  | A122421 | 1451, ... |
| Theodorus's constant |  | A119343 | 17, 173, 1732050807568877293, ... |
