A Pierpont prime is a prime number of the form: 2u3v + 1 for some non-negative integers  u  and  v .



A Pierpont prime of the second kind is a prime number of the form: 2u3v - 1 for some non-negative integers  u  and  v .


The term "Pierpont primes" is generally understood to mean the first definition, but will be called "Pierpont primes of the first kind" on this page to distinguish them.



Task

 Write a routine (function, procedure, whatever) to find Pierpont primes of the first & second kinds.
 Use the routine to find and display here, on this page, the first 50 Pierpont primes of the first kind.
 Use the routine to find and display here, on this page, the first 50 Pierpont primes of the second kind
 If your language supports large integers, find and display here, on this page, the 250th Pierpont prime of the first kind and the 250th Pierpont prime of the second kind.


See also

 Wikipedia - Pierpont primes
 OEIS:A005109 - Class 1 -, or Pierpont primes
 OEIS:A005105 - Class 1 +, or Pierpont primes of the second kind


   5 10$(#~ 1 p:])1+/:~,*//2 3x^/i.20
     2      3       5       7      13      17      19      37      73      97
   109    163     193     257     433     487     577     769    1153    1297
  1459   2593    2917    3457    3889   10369   12289   17497   18433   39367
 52489  65537  139969  147457  209953  331777  472393  629857  746497  786433
839809 995329 1179649 1492993 1769473 1990657 2654209 5038849 5308417 8503057
   5 10$(#~ 1 p:])_1+/:~,*//2 3x^/i.20
     2      3      5       7      11       17       23       31       47       53
    71    107    127     191     383      431      647      863      971     1151
  2591   4373   6143    6911    8191     8747    13121    15551    23327    27647
 62207  73727 131071  139967  165887   294911   314927   442367   472391   497663
524287 786431 995327 1062881 2519423 10616831 17915903 25509167 30233087 57395627