The ranges are 1 100 1 1000 1 10000 1 100000 1 1000000 1 100

The ranges are:

[1, 100]

[1, 1000]

[1, 10000]

[1, 100000]

[1, 1000000]

[1, 10000000]

[7870000000, 7879999999]

[9390000000, 9399999999]

Find:

a)The last five prime numbers in the above 8 ranges

b)The first five prime numbers in ranges vii and viii.

Solution

A prime number is a number which is divisible by 1 and itslef only,

a) To get the list of prime numbers from 1 to 100, write in mathematica first

i) PrimePi[100] the result is 168

Then write

ii) Table[Prime[n], {n, 168}]

The list of primes will be obtained.

The last five prime numbers in [1, 100] are 73 79 83 89 97

The last five prime numbers in [1, 1000] are 971, 977, 983, 991, 997

The last five prime numbers in [1, 10000] are 9931, 9941, 9949, 9967, 9973

The last five prime numbers in [1, 100000] are 99929 , 99961 , 99971 , 99989 , 99991

b)

vii) Write NextPrime[7870000000] will generate primes after 7870000000.

7870000007, 7870000079 , 7870000087, 7870000129, 7870000139

viii) Write NextPrime[9390000000] will generate primes after 9390000000.

9390000007, 9390000029 , 9390000049 , 9390000071 , 9390000097.