Use the sieve in Problem 45a to make a conjecture about primes and multiples of 6.

Data from problem 45

We used a sieve of Eratosthenes in Table 5.2 by arranging the first 100 numbers into 10 rows and 10 columns. Repeat the sieve process for the first 100 numbers by arranging the numbers in the following patterns.

Table 5.2

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1 2 3 7 8 9 13 14 15 1 2 3 8 9 10 15 16 17 c. By 21: 1 2 3 4 5 6 As you are using these sieves, look for patterns. Describe some of the patterns you notice. Do you think that any of these sieves are better than the one shown in Table 5.2? Why or why not? a. By 6: 4 10 b. By 7: 4 11 51 11 5 12 6 12 63 13 7 14