## domingo, 3 de junio de 2012

### To split a number in primes in n ways

23 It is the smallest number that is the concatenation of two primes 2 and 3.
237 is the smallest number that can be separated into two primes in two different ways: 2-37, 23-7
2337 is the smallest number that can be separated into two primes ​​in three different ways: 2-337, 23-37, 233-7
29397 is the smallest number that can be separated into two primes ​​in four different ways: 2-9397, 29-397, 293-97, 2939-7

Hence we have the sequence 23, 237, 2337, 29397
What is the next term in this sequence?

The smallest square that can be divided into two primes is 25
52  = 25  and 25 can be divided into two primes 2-5
772 = 5929  and this is the smallest square that  can be divided into two primes in two different ways: 59-29 and 5-929
15492 = 2399401 and this is the smallest square that can be divided into two primes ​​in three different ways: 2399-401, 23-99401 and 2-399401.

230772 = 532547929 and this is the smallest square that can be divided into two primes ​​in four different ways: 5-32547929 ,  53-2547929 ,  532547-929 and  5325479-29

Hence we have the sequence 5, 77, 1549, 23077

What is the next term in this sequence?