If there is only one composite number between two prime numbers, they are called twin primes. Twin primes are two prime numbers with a two-digit disparity between them. Since the discrepancy between the two numbers (5 – 3 = 2), (3,5) is a twin prime. Prime twin or prime pair are some of the other names given to twin primes. Here you can also read about prime numbers.
Properties of Twin Primes
Below are a few primary properties of twin numbers stated:
- (2,3) are not categorized as twin primes or numbers, since there is no composite number in between them and the difference between the two primes is not equal to 2 but less than that.
- 5 is the only prime number that is available and exists in two different pairs of numbers.
- Every prime pair other than numbers 3,5 is in the form of (6n-1, 6n+1), where n is any estimated as any natural number.
- The sum of every prime number pair existing apart from (3,5) is divisible by the number 12.
What are Coprime numbers?
A co-prime number is a set of numbers or integers with just one common factor, i.e. their highest common factor (HCF) is 1. Relatively prime or mutually prime numbers are examples of coprime numbers. There must be two numbers to form co-primes.
Properties of Co-Prime Numbers
Some of the essential and fundamental properties of coprime numbers are stated as follows.
- 1 is coprime with every number existing in the number system.
- Any two prime numbers that are coprime to each other, as every prime number has only two factors 1 and the number itself, the only common factor of any two prime numbers will be only the number 1. For instance, 2 and 3 are two given prime numbers. Factors of 2 are 1, 2, and factors of 3 are 1, 3 respectively. The only common factor is 1 and consecutively they are coprime.
- Any two successive numbers or integers in the number system are always coprime to each other. Take any consecutive numbers such as 2, 3, or 3, 4 or 5, 6, and so on, all of them will have 1 as their HCF or highest common factor.
- The sum of any two coprime numbers is always coprime with themselves. 2 and 3 are coprime and have 5 as their sum that is 2+3 and 6 as the product 2×3. Therefore, 5 and 6 are co-prime to each other when solved.
- Two even numbers on a given number line can never form a coprime pair. While all the even numbers have a common factor as number 2.
- If two numbers in a number line have their unit digits like 0 and 5, then they are not coprime to each other. For instance, 10 and 15 are not coprime since their HCF is 5 nor is it divided by 5.
Co-prime and Twin Prime Numbers
Co-prime numbers are those whose HCF (highest common factor) is only 1 or two numbers whose only common factor is 1 are named as co-prime numbers. On the other hand, twin prime numbers are those prime numbers whose difference is always the number 2. For instance, 3 and 5 are both named as twin prime numbers.
- Twin numbers are always prime numbers while the coprime numbers can be named as the composite numbers as well.
- The difference between any two given twin primes is always the number 2 while the difference between two co-primes can be any existing number.
- All the pairs of twin prime numbers also share the properties of coprime, while all coprime numbers may or may not be called twin primes.
- 1 forms a coprime pair with every number on the number line, while it forms a twin prime pair with only number 3.