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Term

Twin Prime

Primes p such that p ± 2 is also prime (3, 5, 7, 11, 13, 17, 19, 29, 31, …).

2,448 numbers tagged.

A twin prime is a prime \(p\) such that \(p + 2\) or \(p - 2\) is also prime. Twin primes come in pairs: \((3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73)\).

The Twin Prime Conjecture asserts there are infinitely many twin prime pairs. Despite enormous numerical evidence and partial progress (notably Yitang Zhang's 2013 proof that there are infinitely many primes within a bounded gap), the conjecture remains open.

The sum of reciprocals of twin primes converges to Brun's constant \(B \approx 1.902160583104\), in stark contrast to the divergent sum of reciprocals of all primes.

17,293 17,387 17,389 17,417 17,419 17,489 17,491 17,579 17,581 17,597 17,599 17,657 17,659 17,681 17,683 17,747 17,749 17,789 17,791 17,837 17,839 17,909 17,911 17,921 17,923 17,957 17,959 17,987 17,989 18,041 18,043 18,047 18,049 18,059 18,061 18,119 18,121 18,131 18,133 18,251 18,253 18,287 18,289 18,311 18,313 18,521 18,523 18,539 18,541 18,911 18,913 18,917 18,919 19,079 19,081 19,139 19,141 19,181 19,183 19,211 19,213 19,379 19,381 19,421 19,423 19,427 19,429 19,469 19,471 19,541 19,543 19,697 19,699 19,751 19,753 19,841 19,843 19,889 19,891 19,961 19,963 19,991 19,993 20,021 20,023 20,147 20,149 20,231 20,233 20,357 20,359 20,441 20,443 20,477 20,479 20,507 20,509 20,549 20,551 20,639 20,641 20,717 20,719 20,747 20,749 20,771 20,773 20,807 20,809 20,897 20,899 20,981 20,983 21,011 21,013 21,017 21,019 21,059 21,061 21,191 21,193 21,317 21,319 21,377 21,379 21,491 21,493 21,521 21,523 21,557 21,559 21,587 21,589 21,599 21,601 21,611 21,613 21,647 21,649 21,737 21,739 21,839 21,841 22,037 22,039 22,091 22,093 22,109 22,111 22,157 22,159 22,271 22,273 22,277 22,279 22,367 22,369 22,481 22,483 22,541 22,543 22,571 22,573 22,619 22,621 22,637 22,639 22,697 22,699 22,739 22,741 22,859 22,861 22,961 22,963 23,027 23,029 23,039 23,041 23,057 23,059 23,201 23,203 23,291 23,293 23,369 23,371 23,537 23,539 23,561 23,563 23,627 23,629 23,669 23,671 23,687 23,689 23,741 23,743 23,831