The following questions have come from students over the years. Explore these questions with a partner. After your exploration, summarize and justify your findings.
a. Of the first 100 numbers, 25 are prime. How many of the second hundred numbers will be prime? Will the frequency (density) of prime numbers increase, decrease, or stay at about 25 percent as the numbers get larger and larger?
b. Can you predict when twin primes will occur? How many are there in the first 100 numbers? Will there be the same number of twin primes in the next 100 numbers?
c. The largest difference between two prime numbers less than 100 is 8; it is between the 89 and 97. What is the largest difference you can find between any two prime numbers?
d. Are there more primes with a 1, a 3, a 7, or a 9 in the ones place?
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