### ThurmNumbers

MathBabbler's MBNA (MathBabbler Number Analyst) is a collection of programs that "categorize" numbers. There too many categories to enumerate, but some example categories are: prime or composite; even or odd; evil or odious; happy or unhappy; is Friedman; is palindromic; and so on.

MathBabbler wanted his own category of number so he defined the ThurmNumber. ThurmNumbers are numbers that when represented in score plus number format have a prime score and prime plus number. The smallest ThurmNumber is 42 (2 score 2; 2 is prime); 43 is a ThurmNumber (2 score 3; both 2 and 3 are prime); 87 (4 score 7) is not a ThurmNumber because 4 is not prime; 100 (5 score 0) is not a ThurmNumber because 0 is not prime.

```    42,    43,    45,    47,    51,    53,    57,    59,
62,    63,    65,    67,    71,    73,    77,    79,
102,   103,   105,   107,   111,   113,   117,   119,
142,   143,   145,   147,   151,   153,   157,   159,
222,   223,   225,   227,   231,   233,   237,   239,
262,   263,   265,   267,   271,   273,   277,   279,
342,   343,   ,   347,   351,   353,   357,   359,
382,   383,   385,   387,   391,   393,   397,   399,
462,   463,   465,   467,   471,   473,   477,   479,
582,   583,   585,   587,   591,   593,   597,   599,
622,   623,   625,   627,   631,   633,   637,   639,
742,   743,   745,   747,   751,   753,   757,   759,
822,   823,   825,   827,   831,   833,   837,   839,
862,   863,   865,   867,   871,   873,   877,   879,
942,   943,   945,   947,   951,   953,   957,   959,
1062,  1063,  1065,  1067,  1071,  1073,  1077,  1079,
1182,  1183,  1185,  1187,  1191,  1193,  1197,  1199,
1222,  1223,  1225,  1227,  1231,  1233,  1237,  1239,
1342,  1343,  1345,  1347,  1351,  1353,  1357,  1359,
1422,  1423,  1425,  1427,  1431,  1433,  1437,  1439,
1462,  1463,  1465,  1467,  1471,  1473,  1477,  1479,
1582,  1583,  1585,  1587,  1591,  1593,  1597,  1599,
1662,  1663,  1665,  1667,  1671,  1673,  1677,  1679,
1782,  1783,  1785,  1787,  1791,  1793,  1797,  1799,
1942,  1943,  1945,  1947,  1951,  1953,  1957,  1959,
2022,  2023,  2025,  2027,  2031,  2033,  2037,  2039,
2062,  2063,  2065,  2067,  2071,  2073,  2077,  2079,
2142,  2143,  2145,  2147,  2151,  2153,  2157,  2159,
2182,  2183,  2185,  2187,  2191,  2193,  2197,  2199,
....,  2557,  ....,  2799,  ....,  2987,  ....,  2999,
....,  3031,  ....,  3265,  ....,  3599,  ....,  3827,
....,  3993,  ....,  3997,  3999,  ....,  5151,  ....,
8191,  ...., 73437, ....., 766667, .....
```

There were 30 nBABs (number Basic Arithmetic Bits) for ThurmNumbers when this collection was created on 20 July 2009.

MathBabbler wrote a C++ program to print all ThurmNumbers between 0 and 99,999. 5352 of the 100,000 numbers are ThurmNumbers and 871 of them are prime numbers.

``` + added 225 on 22 July 2009 + added 599 on 26 July 2009 + added 1787 on 17 September 2009 + added 942 on 16 October 2009 + added 103 on 22 October 2009 + added 107 on 10 November 2009 + added 111 on 17 November 2009 + added 2999 on 23 November 2009 + added 142 on 29 November 2009 + added 143 on 29 November 2009 + added 3031 on 30 November 2009 + added 1791 on 15 December 2009 + added 1947 on 23 December 2009 + added 73437 on 08 February 2010 + added 1799 on 16 February 2010 + added 145 on 11 March 2010 + added 343 on 19 March 2010 + added 2799 on 01 April 2010 + added 147 on 13 April 2010 + added 1942 on 13 July 2010 + added 2182 on 02 August 2010 + added 399 on 19 December 2010 + added 157 on 21 June 2011 + added 1599 on 24 July 2011 + added 3265 on 17 December 2011 + added 2557 on 09 February 2012 + added 1071 on 14 May 2012 + added 151 on 04 October 2012 + added 223 on 17 October 2012 + added 2987 on 02 May 2013 + added 1433 on 13 May 2013 + added 237 on 04 July 2013 + added 347 on 13 December 2013 + added 5151 on 10 January 2014 + added 766667 on 23 January 2014 + added 159 on 07 February 2014 + added 3827 on 09 February 2014 + added 279 on 15 March 2014 + added 273 on 15 March 2014 + added 8191 on 27 March 2014 + added 2063 on 05 April 2014 + added 1197 on 05 April 2014 + added 3993 on 22 July 2014 + added 3997 on 26 July 2014 + added 3999 on 27 July 2014 + added 3599 on 18 December 2014 + added 4225 on 24 February 2015 + added 6999 on 25 February 2015 + added 2031 on 08 March 2015 + added 9999 on 07 May 2015 + added 227 on 10 May 2015 + added 2027 on 13 September 2015 + added 263 on 16 September 2015 + added 239 on 16 September 2015 + added 2033 on 28 September 2015 + added 93039 on 18 November 2015 + added 1597 on 23 November 2015 + added 4799 on 06 January 2016 + added 3983 on 06 January 2016 + added 93839 on 19 January 2016 + added 3033 on 20 January 2016 + added 4837 on 24 January 2016 + added 3023 on 27 January 2016 + added 262 on 07 April 2016 + added 265 on 07 April 2016 + added 267 on 07 April 2016 + added 271 on 12 April 2016 + added 277 on 12 April 2016 + added 95759 on 22 May 2016 + added 342 on 09 July 2016 + added 345 on 17 July 2016 + added 99399 on 08 August 2016 + added 99999 on 08 August 2016 + added 32543 on 11 August 2016 + added 4222 on 01 September 2016 + added 351 on 08 September 2016 + added 353 on 15 September 2016 + added 357 on 30 October 2016 + added 359 on 27 December 2016 + added 382 on 02 January 2017 + added 383 on 02 January 2017 + added 385 on 03 January 2017 + added 387 on 03 January 2017 + added 72627 on 07 January 2017 + added 391 on 26 January 2017 + added 393 on 26 January 2017 + added 397 on 01 February 2017 + added 15151 on 16 May 2017 + added 73837 on 05 June 2017 + added 74547 on 06 June 2017 + added 75357 on 08 June 2017 + added 75957 on 09 June 2017 + added 76067 on 10 June 2017 + added 76467 on 10 June 2017 + added 76667 on 10 June 2017 + added 77077 on 11 June 2017 + added 77277 on 11 June 2017 + added 2551 on 18 July 2017 + added 78387 on 09 August 2017 + added 78587 on 10 August 2017 + added 79797 on 10 August 2017 + added 32142 on 05 September 2017 + added 462 on 07 January 2018 + added 463 on 08 January 2018 + added 465 on 03 March 2018 + added 467 on 03 March 2018 + added 951 on 08 March 2018 + added 471 on 17 May 2018 + added 477 on 25 May 2018 ```