Semiprimes in the headlines
- Do you know what a semiprime is?
- If I concentrate I may remember what a prime is.
- 21 is a semiprime since it is the product of two prime numbers.
- You mean 3 and 7?
- 22 is also a semiprime.
- Get out of here!
- 2 and 11 gives 22.
- Are there more pairs of consecutive numbers that are semiprimes?
- There is one pair before 21 and 22.
- And after?
Problem source: math hombre.
January 21st, 2010 at 12:07 am
The semiprimes page is giving me an error 404 so I’ll post my findings here.
2 are found before 21,22:
9,10
14,15
And a number are found after:
25,26
33,34,35
38,39
57,58
85,86,87
93,94,95
118,119
121,122,123
133,134
141,142,143
145,146
158,159
177,178
201,202,203
205,206
213,214,215
217,218,219
253,254
298,299
301,302,303
326,327
334,335
361,362
381,382
393,394,395
…and many many more. The “three in a row” ones are especially neat – it’s a pretty fun coincidence that 3×11, 2×17, and 5×7 produce consecutive semiprime products. I’m surprised that these three-in-a-row groups appear relatively often.