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IMPORTANT
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If a+b+c=66 and ab+bc+ca=1071, where a,b and c are all prime numbers. Find the value of abc.

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Important Questions on Number System

HARD
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 2
The positive integers A, B, A-B and A+B are all prime numbers. The sum of these four primes is
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 3
For how many positive integers a'' is a4-3a2+9 a prime number?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 4
If n is a positive integer greater than 1, then n4+4n is a _________ number.
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 5
What is the smallest positive integer x for which x2-x+5 is not a prime?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 6
What is the smallest composite number generated by p2-p-1, where p is a prime?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 7
Some prime numbers are 1 more than a square, as in 42+1=17. How many primes p≤100 are of the form p=n2+1?
EASY
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 8
How many prime numbers x satisfy 300<x<700?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.1>Q 9
The number of pairs of prime numbers (p, q) satisfying the condition 51100<1p+1q<56 will be