page 259 Burton (end of 11-2)

1, 2 (omit the words The only ) , 3 but change to both x and y cannot be perfect squares. ,11 (again omit The only )

Additionally:

Use software to investigate the distribution of primes. Specifically, develop a table showing intervals of length 100, starting at x=0 and going to 1000 (so 10 entries). The table should show the number of primes in each interval and also the cumulative number of primes from 2 to the higher end of the interval. So three columns:

interval # primes in interval total primes from 2 to end of interval

[2,100 ] 25 25

[101,200] 21 46

[201,300] 16 62

[901,1000]

How many are there between 10,000,001 and 10,000,100 ?

What does all this data suggest?