What is a prime number, what is a factor, what is a factor and a prime number

Prime number. What is a prime number?That is, in all integers greater than 1, there is no other divisor except 1 and itself, and this integer is called a prime number, and a prime number is also called a prime number.

This final rule is only a literal explanation. Is it possible to have an algebraic formula in which the value of the algebraic formula substituted is prime when the number represented by letters is any specified value?

The distribution of prime numbers is irregular and often incomprehensible. For example, are prime numbers, but 301 and 901 are composites.

Someone has done such a check: 1 2 + 1 + 41 = 43, 2 2 + 2 + 41 = 47, 3 2 + 3 + 41 = 53 ......So there can be a formula: if a positive number is n, then the value of n 2+n+41 must be a prime number.

This equation holds until n=39. But when n=40, the formula is not true, because 40 2 + 40 + 41 = 1681 = 41*41.

Férmat, known as "the greatest French mathematician of the 17th century", also studied the properties of prime numbers. He found that if fn=2 (2 n), then when n is equal to , fn is given separately, which are all prime numbers, and since f5 is too large (f5=14292967297), he directly guessed that fn is prime for all natural numbers.

However, it was on F5 that went wrong!Sixty-seven years after Fermat's death, the 25-year-old Swiss mathematician Euler proved that f5 = 14292967297 = 641*6700417 is not a prime number, but a composite number.

What's even more interesting is that in the future, mathematicians never found any fn values that were prime, all of them were composite numbers. At present, due to the large square opening, there is very little that can be proven. Now mathematicians have obtained the maximum value of fn as:

n=1495。This is a very astronomical number, with 10 10,584 digits, and although it is very large, it is not a prime number. Prime numbers and Fermat made a big joke!

In the 17th century, there was also a French mathematician named Mason, who once made a conjecture: 2 p-1 algebraic formula, when p is a prime number, 2 p-1 is a prime number. He calculated:

When p, the values of the resulting algebraic equations are all prime, and later, Euler proved that 2 p-1 is prime when p=31.

There are still p three Merson numbers left, which have not been verified for a long time because they are too large. 250 years after Mason's death, the American mathematician Kohler proved that 2 67-1 = 193707721*761838257287 is a composite number. This is the ninth Mason number.

In the 20th century, it was proved that the 10th Mersen number is a prime number, and the 11th Mersen number is a composite number. The chaotic arrangement of prime numbers also makes it difficult for people to find the laws of prime numbers.

Now, the largest Masonne number that mathematicians have found is a number with 378632 digits: 2 1257787-1. Although mathematics can find a large number of prime numbers, the laws of prime numbers still cannot be followed.

The first 50 million prime numbers.

Table of prime numbers up to 10,000.

A prime number is a factor that has only 1 and itself is its factor, and nothing else.

A factor is a divisor of a number to another, e.g. 4 is a divisor of 8, and 4 is the factor of 8.

Prime numbers are also known as prime numbers. A natural number greater than 1, which is not divisible by other natural numbers except 1 and itself, is called a prime number; Otherwise, it is called a composite number.

Factor, or divisor, is a mathematical noun. Definition: The quotient of the integer a divided by the integer b(b≠0) is exactly an integer and there is no remainder, so we say that b is the factor of a. 0 is not a factor of 0.

Characteristics of factors: The number of factors of a number is finite, of which the smallest factor is 1, and the largest factor is itself.

For example, the factor of 10 is , where the smallest factor is 1 and the largest factor is 10. (1 is the factor of all non-0 natural numbers).

The factor is the quotient of the integer a divided by the integer b(b≠0) exactly the integer and no remainder.

Prime numbers are also known as prime numbers.

A natural car envy number greater than 1.

Numbers other than 1 and itself that are not divisible by other natural numbers are called prime numbers; Otherwise, it is called a composite number.

A natural number is a number of things that are used to measure things or to represent the order of things. i.e. digital 0, 1, 2, 3, 4 ......The number represented. Natural numbers start with 0 and follow each other to form an infinite collective.

Natural numbers are orderly, and infinite are closed. The assignment states are even and odd, composite and prime, etc.

Prime numbers are also known as prime numbers. A natural number greater than 1 that is not divisible by other natural numbers except 1 and itself is called a prime number. The smallest prime number is 2, which is also the only even prime number.

The factor means that the quotient of the integer a divided by the integer b(b≠0) is exactly an integer and there is no remainder, so we say that b is the factor of a.

Prime numbers: There are no factors other than 1 and themselves.

Factor: An integer is divisible by another integer, and the latter is the factor of the former.

What is a prime number, a factor?

Good number of quality deficiency: In layman's terms, it is a number that cannot be divisible by 2, which is the number of quality and lead.

Factor: Dividing an integer by another integer, the quotient obtained is still an integer, and another integer is a factor of an integer, for example, 8 divided by 4 is equal to 2, and 4 is a factor of 8.

1. Different definitions.

1. Factor. Or called a divisor, the quotient of the integer a divided by the integer b(b≠0) is exactly an integer and there is no remainder, we say that b is the factor of a. 0 is not a factor of 0.

2. Prime factor.

In number theory, it refers to a prime number that is divisible by a given positive integer. In addition to 1, a matter and two positive integers that have no other common prime factor are called coprime. Because 1 has no quality factor, 1 is coprime with any positive integer (including 1 itself).

The factorization of positive integers can be expressed as a series of prime factors multiplied, and the quality factors such as repetitions can be expressed exponentially.

Second, the examples are different.

1. Factor. 1) The number of positive factors of a non-zero bright natural number is finite, the smallest of which is 1 and the largest is itself. The number of multiples of a non-zero natural number is infinite.

2) 2 is the smallest prime number.

3) 4 is the smallest composite number.

2. Prime factor.

1) 1 There is no quality factor.

2) 5 has only 1 quality factor, 5 itself. (5 is a prime number) 3) The prime factors of 6 are 2 and 3. (6 = 2 3) Third, the calculation method is different.

1. Factor. Short division:

Find the greatest common factor between 12 and 18.

The factor of 12 has .

The factor of 18 has .

The common factor between 12 and 18 is .

So the greatest common factor between 12 and 18 is 6.

2. Prime factor.

For example, 8=2 2 2, 2 is the prime factor of 8.

12 = 2 2 3, 2 and 3 are the prime factors of 12.

Expressing an equation in the form of 12=2 2 3 is called factoring prime factors.

The quotient of the integer a divided by the integer b(b≠0) is exactly an integer without a remainder, so b is said to be a factor of a. 0 is not a factor of 0. A prime number is a natural number that is greater than 1 and has no other factors than 1 and itself.

Factor: The quotient of the integer a divided by the integer b(b≠0) is exactly an integer and there is no remainder, so we say that b is the factor of a. 0 is not a factor of 0.

Prime number: In a natural number greater than 1, a natural number that has no other factors than 1 and itself.

A prime number is divisible by a number other than 1 and itself, and this is a single number.

Coprime refers to two natural numbers, and there is no other common factor except 1, so these two numbers are said to be coprime. Two numbers that are coprime are not necessarily prime. For example, 4 and 9 are coprimous, but 4 and 9 are both composites.

Both the factor and the common factor are specific numbers, both relative to other numbers. A factor is relative to another number.

For example, if 3 is a missing number of 6, note that this cannot be simplified to say that 3 is a factor.

The common factor is relative to two or more other numbers, such as 3 is the common factor of 6 and 9, and 2 is the common factor of 4 and 6.