semiprime

A semiprime is the product of two primes, which is sometimes called a P2 or a 2-almost prime. The largest known factored semiprime is always the square of the largest known prime. Historically this has also been the largest proven semiprime. It is conceivable, but unlikely, that we may someday be able to show a larger number is composite, and has only two prime divisors.

Small examples of proven, unfactored, semiprimes can be easily constructed (these have been called interesting semiprimes). In 2005 Don Reble gave the following example.

                2354024638195369096484615970884339
82036445614754361975807879103660168355054945730773
42501320913482376791383651754310523953671977852263
05983060913117780151701847341955178208368597048273
68514883246698096782642412942691870383755436538198
72025816440552072944392812834659892991483861033331
19266471392173618443929665694168419491445893554508
31214521115967827260963610250123042880750137421428
79482094899227940491745687352778980891233285140985
59487995775109530064742516289155842487937324115166
99547999240384456822944006777458824969177192912226
96763552830787649258185446654768755654506771225332
40801191691993850537069266814811421303138978077711
47801770048711465135160176473705129584837331514039
79970908037943150798569535461884916441725214274709
51375250077003634182703827942144576309122358369456
49158842746771077588428040839475449415159451169198
34042566389996135670147270228034728379156641389487
95302353410201541057681970330841514731793742263071
86150307934745502893756679402305608524968489170554
18564170025029457397529187683879234264025678162912
22511465758828944973345013184363023296235457948241

Related pages (outside of this work)

• Don Reble's Example