SOLUTION: What comes next in the sequence 2,3,7,23,?

2,3,7,23, are all prime numbers, so we look at the primes
and the differences between each one and the next larger prime.

We start with the first prime, 2.  After that,

Each term is the smallest prime that differs from the next 
prime by more than any of the smaller primes differed from 
their next primes.

We list the prime numbers, and take the difference between the
next prime and it.  When there is an increase in that difference, 
that prime is the next term.

2, difference between 3 and 2 is 1, considered an increase, so 1st term = 2
3, difference between 5 and 3 is 2, an increase over 1, so 2nd term = 3    
5, difference between 7 and 5 is 2. 
7, difference between 11 and 7 is 4, an increase over 2, so 3rd term = 7 
11, difference between 13 and 11 is 2. 
13, difference between 17 and 13 is 4. 
17, difference between 19 and 17 is 2. 
19, difference between 23 and 19 is 4. 
23, difference between 29 and 23 is 6, an increase over 4, so 4th term = 23 
29, difference between 31 and 29 is 2. 
31, difference between 37 and 31 is 6. 
37, difference between 41 and 37 is 4. 
41, difference between 43 and 41 is 2. 
43, difference between 47 and 43 is 4. 
47, difference between 53 and 47 is 4. 
53, difference between 59 and 53 is 6. 
59, difference between 61 and 59 is 2.
61, difference between 67 and 61 is 6. 
67, difference between 71 and 67 is 4. 
71, difference between 73 and 71 is 2. 
73, difference between 79 and 73 is 6. 
79, difference between 83 and 79 is 4. 
83, difference between 89 and 83 is 6. 
89, difference between 97 and 89 is 8, an increase over 6, so 5th term = 89 

Answer = 89.

Edwin

    2,  3,  7,  23
Diff = 1  4   16

23 is obtained by taking off the comma between 2 and 3, the two first members.


Hence, the next after 23 is 37, which is obtained by taking off the comma between the next two members 3 and 7.

Ha-ha-ha