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P Pankaj Sanodiya
Five pairs of prime numbers less than 20 whose sum is divisible by 5 are : 2+3=5 2+13=15 3+17=20 7+13=20 19+11=30

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P Pankaj Sanodiya
(a) 21 = 3 + 7 + 11 (b) 31 = 5 + 7 + 19 (c) 53 = 3 + 19 + 31 (d) 61 = 11 + 19 + 31

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P Pankaj Sanodiya
Seven consecutive composite numbers less than 100 so that there is no prime number between them are : Between 89 and 97, both of which are prime numbers, there are 7 composite numbers. They are: 90,91,92,93,94,95,96

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P Pankaj Sanodiya
(a) 23,23=1 23,23=23 123,23=1 23,23=23 1 23 has only two factors, 1 and 23. Therefore, it is a prime number. (b) 51,51=1 51,51=3 1751,51=1 51,51=3 17 51 has four factors, 1, 3, 17, 51. Therefore, it is not a prime number. It is a composite number. (c) 37 It has only two factors, 1 and 37. Therefore, it is a prime number. (d) 26 26 has four factors (1, 2, 13, 26). Therefore, it is not a...

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P Pankaj Sanodiya
three pairs of prime numbers whose difference is 2 are : 3,5 41,43 and 71,73

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P Pankaj Sanodiya
(a) 44 = 37 +7 (b) 36 = 31 +5 (c) 24 = 19 +5 (d) 18 = 11 +7

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P Pankaj Sanodiya
Prime numbers between 1 and 10 are 2, 3, 5, and 7. Among these numbers, 7 is the greatest.

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P Pankaj Sanodiya
Prime numbers less than 20 are : 2, 3, 5, 7, 11, 13, 17, 19 Composite numbers less than 20 are : 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

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P Pankaj Sanodiya
(a) False, Because the sum of two odd number is even and the sum of even number and an odd number is odd, so the sum of three odd numbers is odd.      for example :      3 + 5 + 7 = 15, i.e., odd (b) True, as the sum of two odd number is even a sum of two even number is even.       for example :       3 + 5 + 6 = 14, i.e., even (c) True because the product of two odd number is odd and product...

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P Pankaj Sanodiya
(a) the sum of any two Odd numbers is always even. for e.g. 3 + 5 = 8 and 9 + 7 = 16 (b) the sum of any two Even numbers is always even. for e.g. 2 + 4 = 6 and 8 + 4 = 12
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