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.
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