Which of the following is TRUE regarding prime numbers less than 100? A: Between any two consecutive prime numbers there cannot be more than 5 composite numbers. B: Among the prime numbers below 100, integers with the unit digit ‘3’ are maximum. C: Any number of the form n + n2 – 3 is always a composite number.
Which of the following is TRUE regarding prime numbers less than 100? A: Between any two consecutive prime numbers there cannot be more than 5 composite numbers. B: Among the prime numbers below 100, integers with the unit digit ‘3’ are maximum. C: Any number of the form n + n2 – 3 is always a composite number. Correct Answer B only
GIVEN:
Prime number less than 100
CONCEPT:
Properties of prime numbers and composite numbers
CALCULATION:
A. Since, we know that unit digit of prime number can be 1, 2, 3, 5, 7 and 9. When we observe the list of prime number less than 100, we find maximum number of composite numbers between any two consecutive prime numbers is 5. But we have numbers like 89 and 97 between which we have 7 consecutive composite numbers. Thus statement A is false.
B. All the prime numbers less than 3 are
Total prime number with unit digit ‘1’ = 11, 31, 41, 61, 71
Total prime number with unit digit ‘2’ = 2
Total prime number with unit digit ‘3’ = 3, 13, 23, 43, 53, 73, 83
Total prime number with unit digit ‘5’ = 5
Total prime number with unit digit ‘7’ = 7, 17, 37, 47, 67, 97
Total prime number with unit digit ‘9’ = 19, 29, 59, 79, 89
C. Any number of the form n + n2 – 3
Put n = 2
= 2 + 22 – 3
= 2 + 4 – 3
= 3 (Prime number)
∴ Only A and B follows
