Question

In how many pairs of consecutive prime numbers from 1 to 100. does a
difference of 6 occur?
(1) 2 (2) 7 (3) 4 (4) 10​

Answer 1

${\mathcal{\red{ANSWER}}}$

Required No. of pairs are = 7.

${\mathcal{\red{EXPLANATION}}}$

The prime Numbers from 1 to 100 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Pairs of consecutive prime numbers in which difference of 6 occurs:

$\tt{(23,\;29)}$

$\tt{(31,\;37)}$

$\tt{(47,\;53)}$

$\tt{(53,\;59)}$

$\tt{(61,\;67)}$

$\tt{(73,\;79)}$

$\tt{(83,\;89)}$

So, required no. of pairs = 7.

Answer 2

$ANSWER \\ </p><p></p><p>Required No. of pairs are = 7. \\ </p><p></p><p>{\mathcal{\red{EXPLANATION}} }EXPLANATION \\ </p><p></p><p>The prime Numbers from 1 to 100 are: \\ </p><p></p><p>2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. \\ </p><p></p><p>Pairs of consecutive prime numbers in which difference of 6 occurs:</p><p> \\ </p><p>\tt{(23,\;29)}(23,29) \\ </p><p></p><p>\tt{(31,\;37)}(31,37) \\ </p><p></p><p>\tt{(47,\;53)}(47,53) \\ </p><p></p><p>\tt{(53,\;59)}(53,59) \\ </p><p></p><p>\tt{(61,\;67)}(61,67) \\ </p><p></p><p>\tt{(73,\;79)}(73,79) \\ </p><p></p><p>\tt{(83,\;89)}(83,89) \\ </p><p></p><p>So, required no. of pairs = 7. \\ </p><p></p><p>$