## Friday, January 19, 2007

### Tupper's Self-Referential Formula

J. Tupper concocted the amazing formula
$1/2 < \lfloor mod(\lfloor y/(17) \rfloor 2^(-17 \lfloor x \rfloor -mod(\lfloor y \rfloor,17)),2) \rfloor$,

where $\lfloor x \rfloor$ is the floor function and mod(b, m) is the mod function, which, when graphed over 0 ≤ x ≤ 105 and n ≤ y ≤ n + 16 with
n = $960,939,379,918,958,884,971,672,962,127,$
$852,754,715,004,339,660,129,306,651,505,519,$
$271,702,802,395,266,424,689,642,842,174,350,$
$718,121,267,153,782,770,623,355,993,237,280,$
$874,144,307,891,325,963,941,337,723,487,857,$
$735,749,823,926,629,715,517,173,716,995,165,$
$232,890,538,221,612,403,238,855,866,184,013,$
$235,585,136,048,828,693,337,902,491,454,229,$
$288,667,081,096,184,496,091,705,183,454,067,$
$827,731,551,705,405,381,627,380,967,602,565,$
$625,016,981,482,083,418,783,163,849,115,590,$
$225,610,003,652,351,370,343,874,461,848,378,$
$737,238,198,224,849,863,465,033,159,410,054,$
$974,700,593,138,339,226,497,249,461,751,545,$
$728,366,702,369,745,461,014,655,997,933,798,$
$537,483,143,786,841,806,593,422,227,898,388,$
$722,980,000,748,404,719$,

gives the self-referential "plot" illustrated above.

## Tuesday, January 16, 2007

### Latest, Greatest Twins in Their Prime

The Twin Internet Prime Search and PrimeGrid distributed computation projects have recently discovered the largest known twin primes, which is a pair of prime numbers separated by two. The pair discovered on January 15th are $2,003,663,613 \times 2^{195,000} ± 1$. The two primes are 58,711 digits long. The discoverer was Eric Vautier from France.