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Term

Chen Prime

Primes p where p + 2 is prime or a semiprime (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, …).

4,236 numbers tagged.

A Chen prime is a prime \(p\) such that \(p + 2\) is either prime or a semiprime (a product of two primes). Every twin prime's smaller member is automatically a Chen prime; the class also includes primes like 23, where 25 = 5² is a semiprime.

The name honors Chen Jingrun, whose 1966 theorem — every sufficiently large even number is the sum of a prime and a number with at most two prime factors — remains the closest anyone has come to proving Goldbach's conjecture. The same paper proved there are infinitely many Chen primes, a result standing in for the still-open twin prime conjecture.

2 3 5 7 11 13 17 19 23 29 31 37 41 47 53 59 67 71 83 89 101 107 109 113 127 131 137 139 149 157 167 179 181 191 197 199 211 227 233 239 251 257 263 269 281 293 307 311 317 337 347 353 359 379 389 401 409 419 431 443 449 461 467 479 487 491 499 503 509 521 541 557 563 569 571 577 587 599 617 631 641 647 653 659 677 683 701 719 743 751 761 769 787 797 809 811 821 827 829 839 857 863 877 881 887 911 919 937 941 947 953 971 977 983 991 1,009 1,019 1,031 1,039 1,049 1,061 1,091 1,097 1,109 1,117 1,151 1,163 1,187 1,193 1,201 1,217 1,229 1,259 1,277 1,283 1,289 1,291 1,297 1,301 1,319 1,327 1,361 1,367 1,381 1,399 1,409 1,427 1,439 1,451 1,459 1,471 1,481 1,487 1,499 1,511 1,553 1,559 1,567 1,583 1,601 1,607 1,619 1,621 1,637 1,667 1,669 1,697 1,709 1,721 1,733 1,759 1,777 1,787 1,801 1,847 1,871 1,877 1,889 1,901 1,907 1,913 1,931 1,949 1,979 1,997 2,003 2,017 2,027 2,029 2,039 2,069 2,081 2,087 2,099 2,111 2,129 2,141 2,153 2,179 2,207