Is 1001 a Prime Number?

A number to be identified as a prime number: the number should not have more than two factors, that too only 1 and itself, or else it is a composite number. 1001 is not a prime number, since factors of 1001 are 1,7,11,13,77,91,143 and 1001, where the count of factors is more than two, hence, it is not a prime number.

So, we can say that 1001 is a composite number.

We will now check through various methods to see if 1001 is a prime number or not. Let’s proceed.

• Counting Divisors Method

• Prime Number Chart

• Prime Factorization Method
   

The only condition this method involves is that a particular number is prime if and only if it has two distinct integers as its divisors. In the case of 1001, the distinct divisors are: 1,7,11,13,77,91,143 and 1001. Hence, there exist more than two divisors of 1001. Hence, 1001 is not prime.
 

The list of prime numbers up to 1100 are → 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,

67,71,73,79,83,89,97,101,103,107,109,113,127,131,

137,139,149,151,157,163,167,173,179,

181,191,193,197,199,211,223,227,229,233,

239,241,251,257,263,269,271,277,281,283,293,

307,311,313,317,331,337,347,349,353,359,367

,373,379,383,389,397,401,409,419,421,431,

433,439,443,449,457,461,463,467,479,487,491,

499,503,509,521,523,541,547,557,563,569,

571,577,587,593,599,601,607,613,617,619,631

,641,643,647,653,659,661,673,677,683,691,

701,709,719,727,733,739,743,751,757,769,773,

787,797,809,811,821,823,827,829,839,853

,857,859,863,877,881,883,887,907,911,919,929

,937,941,947,953,967,971,977,983,991,

997,1009,1013,101,1021,1031,1033,1039,1049,

1051,1061,1063,1069,1087,1091,

1093,1097. 

Following the above chart for reference, we can see that 1001 is not in the list. Hence, 1001 is not a prime number.
 

Prime factorization of, 1001

1001 = 7×3×11 

1001 is being easily factored into distinct smaller prime factors, clearly making it a composite number. 

Cryptography: This is the branch which deals with cybersecurity, applying encoding-decoding methods.

• Prime Factorization: The process of breaking down a number into the product of its prime factors only, is called Prime Factorization. 

• Composite numbers: Composite numbers are numbers which have factors more than two.

• Twin prime numbers: Twin primes are those prime number pairs that have a difference of 2.

• Perfect Divisor: Integers that divide into numbers, leaving no remainders behind. 

• Primality: The property of being a prime number, which is a natural number with factors only of itself and 1.