Editing Happy number (section)

==Happy primes==
A <math>b</math>-happy prime is a number that is both <math>b</math>-happy and [[prime number|prime]]. Unlike happy numbers, rearranging the digits of a <math>b</math>-happy prime will not necessarily create another happy prime. For instance, while 19 is a 10-happy prime, 91&nbsp;=&nbsp;13&nbsp;×&nbsp;7 is not prime (but is still 10-happy).

All prime numbers are 2-happy and 4-happy primes, as [[base 2]] and [[base 4]] are happy bases.

===6-happy primes===
In [[base 6]], the 6-happy primes below 1296 = 6<sup>4</sup> are
:211, 1021, 1335, 2011, 2425, 2555, 3351, 4225, 4441, 5255, 5525

===10-happy primes===
In [[base 10]], the 10-happy primes below 500 are
:7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487 {{OEIS|id=A035497}}.

The [[palindromic prime]] {{nowrap|10<sup>150006</sup> + {{val|7426247e75000}} + 1}} is a 10-happy prime with {{val|150,007}} digits because the many 0s do not contribute to the sum of squared digits, and {{nowrap|1<sup>2</sup> + 7<sup>2</sup> + 4<sup>2</sup> + 2<sup>2</sup> + 6<sup>2</sup> + 2<sup>2</sup> + 4<sup>2</sup> + 7<sup>2</sup> + 1<sup>2</sup>}} =&nbsp;176, which is a 10-happy number. Paul Jobling discovered the prime in 2005.<ref>{{cite web |url=http://primes.utm.edu/primes/page.php?id=76550 |title=The Prime Database: 10<sup>150006</sup> + 7426247 · 10<sup>75000</sup> + 1 |author=Chris K. Caldwell |work=utm.edu}}</ref>

{{As of|2010}}, the largest known 10-happy prime is 2<sup>42643801</sup>&nbsp;−&nbsp;1 (a [[Mersenne prime]]).{{Dubious|date=December 2017}} Its decimal expansion has {{val|12,837,064}} digits.<ref>{{cite web |url=http://primes.utm.edu/primes/page.php?id=88847 |title=The Prime Database: 2<sup>42643801</sup> − 1 |author=Chris K. Caldwell |work=utm.edu}}</ref>

===12-happy primes===

In [[base 12]], there are no 12-happy primes less than 10000, the first 12-happy primes are (the letters X and E represent the decimal numbers 10 and 11 respectively)

:11031, 1233E, 13011, 1332E, 16377, 17367, 17637, 22E8E, 2331E, 233E1, 23955, 25935, 25X8E, 28X5E, 28XE5, 2X8E5, 2E82E, 2E8X5, 31011, 31101, 3123E, 3132E, 31677, 33E21, 35295, 35567, 35765, 35925, 36557, 37167, 37671, 39525, 4878E, 4X7X7, 53567, 55367, 55637, 56357, 57635, 58XX5, 5X82E, 5XX85, 606EE, 63575, 63771, 66E0E, 67317, 67371, 67535, 6E60E, 71367, 71637, 73167, 76137, 7XX47, 82XE5, 82EX5, 8487E, 848E7, 84E87, 8874E, 8X1X7, 8X25E, 8X2E5, 8X5X5, 8XX17, 8XX71, 8E2X5, 8E847, 92355, 93255, 93525, 95235, X1X87, X258E, X285E, X2E85, X85X5, X8X17, XX477, XX585, E228E, E606E, E822E, EX825, ...