### MATHEMATICAL NUMBERS

Fundamental Numbers

p = 3.1415926535 8979323846 2643383279 5028841971 6939937510

e = 2.7182818284 59045

Prime Numbers

Prime numbers are those numbers that have no factors other than one and themselves. These numbers now play a very important part in cryptography, and also in SETI (the Search for Extra-Terrestrial Intelligence).

```     PRIME NUMBERS UNDER 1000

1    2    3    5    7   11   13   17   19   23
29   31   37   41   43   47   53   59   61   67
71   73   79   83   89   97  101  103  107  109
113  127  131  137  139  149  151  157  163  167
173  179  181  191  193  197  199  211  223  227
229  233  239  241  251  257  263  269  271  277
281  283  293  307  311  313  317  331  337  347
349  353  359  367  373  379  383  389  397  401
409  419  421  431  433  439  443  449  457  461
463  467  479  487  491  499  503  509  521  523
541  547  557  563  569  571  577  587  593  599
601  607  613  617  619  631  641  643  647  653
659  661  673  677  683  691  701  709  719  727
733  739  743  751  757  761  769  773  787  797
809  811  821  823  827  829  839  853  857  859
863  877  881  883  887  907  911  919  929  937
941  947  953  967  971  977  983  991  997
```

Square Numbers

Square numbers are simply numbers that are the product of a number times itself. The first 100 square numbers are listed below:

```      1     4     9    16    25    36    49    64    81   100
121   144   169   196   225   256   289   324   361   400
441   484   529   576   625   676   729   784   841   900
961  1024  1089  1156  1225  1296  1369  1444  1521  1600
1681  1764  1849  1936  2025  2116  2209  2304  2401  2500
2601  2704  2809  2916  3025  3136  3249  3364  3481  3600
3721  3844  3969  4096  4225  4356  4489  4624  4761  4900
5041  5184  5329  5476  5625  5776  5929  6084  6241  6400
6561  6724  6889  7056  7225  7396  7569  7744  7921  8100
8281  8464  8649  8836  9025  9216  9409  9604  9801 10000
```

You may note that square numbers end only in the digits 0, 1, 4, 5, 6 or 9. Thus if a number ends in 2, 3, 7 or 8 it cannot be square.

Fibonacci Numbers

The first two Fibonacci numbers are one (unity). All the others are computed from the formula:

fb(i) = fb(i-1) + fb(i-2)
The first 30 Fibonacci numbers are listed below:

```     1      1      2      3      5      8     13     21     34     55
89    144    233    377    610    987   1597   2584   4181   6765
10946  17711  28657  46368  75025 121393 196418 317811 514229 832040
```

Fibonacci was an Italian mathematician who lived from about 1175 to 1240 AD. His book Liber Abaci (the Book of the Abacus) helped introduce Hindu-Arabic numerals (0,1,2,3,...) to the western world. In it he also explained the number sequence that is now named after him. These numbers, particularly the first seven, have an intimate relationship to the natural world.