article on base rate fallacy

Bruce Schneier pointed in his blog to the following article on the base rate fallacy: A scanner to detect terrorists by Michael Blastland.  It includes a nicely worked example and an even better graphic.

Recognize your Primes

After reading Tanya Khovanova’s Remember your Primes, I decided to do so.  The description is due to John Conway.

Instead of memorizing all primes below 1000, it is easier to recognize composites:

1.  Multiples of 2, 3, 5, 11 are easily detected.

2.  Squares are known.

3.  All that remains is to memorize 70 “non-trivial” composites (opposed to 168 primes in that range):

91, 119, 133, 161, 203, 217, 221, 247, 259, 287, 299, 301, 323, 329, 343, 371, 377, 391, 403, 413, 427, 437, 469, 481, 493, 497, 511, 527, 533, 551, 553, 559, 581, 589, 611, 623, 629, 637, 667, 679, 689, 697, 703, 707, 713, 721, 731, 749, 763, 767, 779, 791, 793, 799, 817, 833, 851, 871, 889, 893, 899, 901, 917, 923, 931, 943, 949, 959, 973, 989.

1. Remark:

If you are lazy, you can learn primes only up to 100. [...] [Y]ou need to remember only one number: 91.

2. Remark:

If you are very ambitious and plan to learn the primes up to 50,000, then the trick of learning non-trivial composites instead of primes is of no use to you. [...] The turning point is around 11,625: the number of primes below 11,625 equals the number of non-trivial composites below it.

3. As soon as you feel comfortable in the range below 1000 two more classes of composites become trivial to detect: Multiples of 7 and 13, since you can find the residue of a given number modulo 1001 by taking the alternating sum of three-digits.