There is no largest composite number. Nor is there a largest sequence of consecutive composite numbers - those sequences can become arbitrarily long.
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21 and 22 are the first pair.It can be proven that, given any number n, there are sequences of n consecutive composite numbers.
Basically, composite numbers are the non-prime numbers. Take a table of prime numbers, and look for any two prime numbers, one after the other, that have a difference greater than 2. Any numbers in between are consecutive composite numbers. For example, the next prime number after 13 is 17; that makes 14, 15, and 16 three consecutive non-primes, i.e., composite numbers.
A rectangular number is the product of two consecutive integers, that is, n (n + 1). A composite number is a positive integer with more than two factors.
The 13 consecutive numbers from 114 to 126 are composite.The 13 consecutive numbers from 114 to 126 are composite.The 13 consecutive numbers from 114 to 126 are composite.The 13 consecutive numbers from 114 to 126 are composite.
The smallest six consecutive composite integers are:90, 91, 92, 93, 94, 95.(And 96 is also composite, for a run of seven consecutive.)Is that what you were asking ?