by johnnydeep » Tue Mar 30, 2021 3:42 pm
neufer wrote: ↑Tue Mar 30, 2021 2:09 am
https://en.wikipedia.org/wiki/Sexy_prime wrote:
<<
Sexy primes are prime numbers that differ from each other by 6.
- Sexy primes below 500 are:
(5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).
As of October 2019, the largest-known pair of sexy primes was found by P. Kaiser and has 50,539 digits. The primes are:
- p = (520461 × 255931+1) × (98569639289 × (520461 × 255931-1)2-3)-1
p+6 = (520461 × 255931+1) × (98569639289 × (520461 × 255931-1)2-3)+5
...............................................................
Sexy primes can be extended to larger constellations.
E.g., triplets of primes
(p, p+6, p+12) such that p+18 is composite are called sexy prime triplets.
- Sexy prime triplets below 1,000 are:
(7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283), (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659), (727,733,739), (941,947,953), (971,977,983).
in December Norman Luhn & Gerd Lamprecht & Norman Luhn set a record for the largest-known sexy prime triplet with 10,602 digits:
- p = 2683143625525 x 235176+1.
p+6 = 2683143625525 x 235176+7.
p+12 = 2683143625525 x 235176+13.
>>
Sometimes mathematicians appear to have too much time on their hands.
Sexy Primes seem particularly useless to me, let alone "sexy", and not really even very interesting. Same for "sexy prime triples". Perhaps that's why I abandoned the idea of becoming a professional mathematician after getting an MS in math. Now,
consecutive primes {p,p+6} (that is, with no intervening primes), or consecuting primes {p,p+n} for various values of n
do seem interesting. And even more interesting is the "primorial" function, which extends the idea of the factorial to the multiplication of all primes up to and including n. See
https://en.wikipedia.org/wiki/Primorial
[quote=neufer post_id=312030 time=1617070157 user_id=124483]
[quote=XgeoX post_id=312017 time=1617028706 user_id=145282]
[quote]11211 is a Composite Number and can be factored by any of the following numbers.
All the factors of 11211 :
1, 3, 37, 101, 111, 303, 3737, 11211[/quote]
https://www.calculatorsoup.com/calculators/math/prime-number-calculator.php
Warning: it is very addictive![/quote][quote=https://en.wikipedia.org/wiki/Sexy_prime]
<<[b][u][color=#FF0000]Sexy primes are prime numbers that differ from each other by 6.[/color][/u][/b]
[list][b]Sexy primes below 500 are:
(5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).[/b][/list]
As of October 2019, the largest-known pair of sexy primes was found by P. Kaiser and has 50,539 digits. The primes are:
[list][b] p = (520461 × 2[sup]55931[/sup]+1) × (98569639289 × (520461 × 2[sup]55931[/sup]-1)[sup]2[/sup]-3)-1
p+6 = (520461 × 2[sup]55931[/sup]+1) × (98569639289 × (520461 × 2[sup]55931[/sup]-1)[sup]2[/sup]-3)+5[/b][/list]
...............................................................
[b][u][color=#FF0000]Sexy primes can be extended to larger constellations.[/color][/u][/b]
E.g., triplets of primes [b][color=#0000FF](p, p+6, p+12)[/color][/b] such that p+18 is composite are called sexy prime triplets.
[list][b]Sexy prime triplets below 1,000 are:
(7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283), (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659), (727,733,739), (941,947,953), (971,977,983).[/b][/list]
in December Norman Luhn & Gerd Lamprecht & Norman Luhn set a record for the largest-known sexy prime triplet with 10,602 digits:
[list][b][color=#0000FF]p[/color] = 2683143625525 x 2[sup]35176[/sup]+1.
[color=#0000FF]p+6[/color] = 2683143625525 x 2[sup]35176[/sup]+7.
[color=#0000FF]p+12[/color] = 2683143625525 x 2[sup]35176[/sup]+13.[/b][/list]>>[/quote]
[/quote]
Sometimes mathematicians appear to have too much time on their hands. :ssmile: Sexy Primes seem particularly useless to me, let alone "sexy", and not really even very interesting. Same for "sexy prime triples". Perhaps that's why I abandoned the idea of becoming a professional mathematician after getting an MS in math. Now, [b][i]consecutive [/i][/b]primes {p,p+6} (that is, with no intervening primes), or consecuting primes {p,p+n} for various values of n [b][i]do [/i][/b]seem interesting. And even more interesting is the "primorial" function, which extends the idea of the factorial to the multiplication of all primes up to and including n. See https://en.wikipedia.org/wiki/Primorial