1. A prime number is a counting number with exactly two factors, the number itself and the number 1. In the sequence 2, 5, 11, 23, ... each number is obtained by doubling the previous number and adding 1. What is the first number in the sequence that is not a prime number?
2. Suppose a twinner is a number that is both 1 more than a prime number and 1 less than another prime number. For example, 30 is a twinner because 29 and 31 are both prime numbers. What is the sum of the three least twinners?
3. 111 111 is the product of 5 different prime numbers. What is the sum of those 5 prime numbers?
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