number.wiki
Term

Sexy Prime

Primes p such that p ± 6 is also prime — “sexy” from the Latin sex (six).

4,364 numbers tagged.

A sexy prime is a prime \(p\) such that \(p + 6\) or \(p - 6\) is also prime. The name is a pun: the Latin word for six is sex.

Sexy prime pairs: \((5, 11), (7, 13), (11, 17), (13, 19), (17, 23), (23, 29), (31, 37), (37, 43)\). Some primes are both sexy and twin: 5 is twin with 7 and sexy with 11.

There can be sexy prime triplets \((p, p+6, p+12)\) all prime — e.g., (5, 11, 17), (7, 13, 19), (17, 23, 29) — and even quadruplets like (5, 11, 17, 23) and (11, 17, 23, 29). It's conjectured that infinitely many sexy prime constellations exist.

57,781 57,787 57,793 57,803 57,809 57,847 57,853 57,859 57,917 57,923 58,043 58,049 58,061 58,067 58,073 58,147 58,153 58,193 58,199 58,211 58,217 58,231 58,237 58,243 58,363 58,369 58,411 58,417 58,537 58,543 58,549 58,567 58,573 58,579 58,687 58,693 58,699 58,727 58,733 58,757 58,763 58,901 58,907 58,913 58,937 58,943 58,991 58,997 59,023 59,029 59,063 59,069 59,077 59,083 59,107 59,113 59,119 59,233 59,239 59,351 59,357 59,387 59,393 59,399 59,441 59,447 59,453 59,467 59,473 59,561 59,567 59,611 59,617 59,621 59,627 59,663 59,669 59,693 59,699 59,723 59,729 59,747 59,753 59,791 59,797 59,951 59,957 60,077 60,083 60,089 60,101 60,107 60,127 60,133 60,139 60,161 60,167 60,217 60,223 60,251 60,257 60,331 60,337 60,343 60,443 60,449 60,521 60,527 60,601 60,607 60,611 60,617 60,623 60,631 60,637 60,727 60,733 60,757 60,763 60,773 60,779 60,913 60,917 60,919 60,923 60,937 60,943 61,001 61,007 61,051 61,057 61,291 61,297 61,333 61,339 61,357 61,363 61,403 61,409 61,463 61,469 61,487 61,493 61,547 61,553 61,559 61,603 61,609 61,631 61,637 61,643 61,651 61,657 61,667 61,673 61,681 61,687 61,717 61,723 61,729 61,751 61,757 61,813 61,819 61,837 61,843 61,927 61,933 61,961 61,967 61,981 61,987 62,011 62,017 62,047 62,053 62,131 62,137 62,143 62,201 62,207 62,213 62,219 62,297 62,303 62,417 62,423 62,467 62,473 62,477 62,483 62,501 62,507 62,533 62,539 62,591 62,597 62,603 62,627 62,633

← all tags