Find out the next number in the sequence.
2 - 6 - 39916800 - 6227020800 - 355687428096000 - ?
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Your number sequence reads as
2! - 3! - 11! - 13! - 17! - ?
which means that I'd guess the next number would be
19! = 121,645,100,408,832,000.... What I don't understand is if this is the case,
5! = 120 and 7! = 5040 are missing from the sequence.
It is therefore otherwise that
we have 2! - 3! (skip 5!, skip 7!) - 11! - 13! - 17! (skip 19!, skip 23!, skip 29!) - 31! (The patter is that we take factorials of the first two primes, then skip the next two, then take the factorials of the first three primes, then skip the next three, etc.)
In which case the answer is
31! = 8,222,838,654,177,922,817,725,562,880,000,000