All prime numbers other than 2 and 3 can be written as one more than a multiple of 6 or one less than a multiple of 6 and not vice versa. For example, 19 can be written as 6*3 + 1, 23 can be written as 6*4 - 1, 97 can be written as 6*16 + 1 and so on.A number 'n' can be immediately said as composite if it is not in the form of 6*m + 1 or 6*m -1 for some m>=1.
Question
All prime numbers other than 2 and 3 can be written as one more than a multiple of 6 or one less than a multiple of 6 and not vice versa. For example, 19 can be written as 63 + 1, 23 can be written as 64 - 1, 97 can be written as 616 + 1 and so on.A number 'n' can be immediately said as composite if it is not in the form of 6m + 1 or 6*m -1 for some m>=1.
Solution
To determine if a number 'n' is prime or composite, we can use the rule mentioned above.
Step 1: Check if 'n' is equal to 2 or 3. If it is, then 'n' is a prime number.
Step 2: If 'n' is not equal to 2 or 3, check if it can be written in the form of 6m + 1 or 6m - 1, where m is a positive integer greater than or equal to 1.
Step 3: If 'n' can be written in the form of 6m + 1 or 6m - 1, then 'n' is a prime number.
Step 4: If 'n' cannot be written in the form of 6m + 1 or 6m - 1, then 'n' is a composite number.
For example, let's take the number 19:
Step 1: 19 is not equal to 2 or 3.
Step 2: We can write 19 as 63 + 1, which follows the form of 6m + 1.
Step 3: Therefore, 19 is a prime number.
Similarly, we can apply this process to any number to determine if it is prime or composite.
Similar Questions
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number is a whole number greater than 1 that cannot be formed by multiplying two smaller whole numbers. For example, 2, 3, 5, 7, 11, and 13 are prime numbers because they cannot be divided evenly by any other number except 1 and themselves. Prime numbers play a fundamental role in number theory and have various applications in mathematics and computer science, such as in cryptography and prime factorization algorithms.
Try to write each composite number on your list as the sum of two prime numbers.For example: 6 = 3 + 3 and 8 = 3 + 5
Do you have to find all the factors of a number to decide whether it is composite? Explain.
Which one of the following numbers is NOT a prime number?
A prime number is an integer greater or equal to 2 that is only divisible by 1 and by itself. The first few primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 …N is a prime if and only if it is not divisible evenly by any of the numbers from 2 to N−1. Let’s implement this decision as a function.
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