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That there are an infinite number of prime numbers.
Before we look an explanation or proof, we must agree on some points
1. The term number means whole number or integer
2. A Prime number is any number that has only 2 factors (1 and itself).
3. All numbers are either prime or the product of 1 or more primes; try and find a number that you cannot generate as the product of primes (e.g. 8 = 2x2x2; 36 = 2x2x3x3).
Now:
If you take any two or more prime numbers and find their product the resulting number will have the prime numbers used as factors. However, if you add 1 to the number then the prime numbers you used to produce this number will now no longer be factors of this new number.
Example
2,3,5 (first three prime numbers) 2x3x5 = 30
30 +1 =31 - now 2,3 and 5 are not factors as you will always have a remainder of 1 if you divide by any of the three original prime factors (2,3 or 5).
If you take all of the known prime numbers and find the product of all of these prime numbers we get a new number (call it Product of Primes or PP), PP will have all the know primes as its factors. If we now add one to PP (PP + 1=N) we will get a number, N, that will have none of the known primes as a factor. If we say that the highest value prime number known (that we used to generate PP) is Pi then N must either be prime or have a prime factor greater than Pi and thus Pi is not the highest prime number. Therefore there are an infinite number of prime numbers.
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How many prime numbers are they and what are they?
Prime numbers are positive integers that only have two factors. In theory, there is an infinite amount of them.
State the characterictics prime numbers share?
The crucial importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic.
What was the contribution of euclid in number system?
Euclid contributed to number theory, which is the study of integers. He worked on prime numbers and divisibility. He proved the infinitude of prime numbers, which had not been proven before.
How is the number theory different from arithmetic?
Arithmetic can be written as two different products of prime numbers. haha
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What is euclids theory?
need a simple explanation of Euclids theory.
How many prime numbers are they and what are they?
Prime numbers are positive integers that only have two factors. In theory, there is an infinite amount of them.
What has the author Y Motohashi written?
Y. Motohashi has written: 'Sieve Methods and Prime Number Theory (Lectures on Mathematics and Physics Mathematics)' 'Lectures on sieve methods and prime number theory' -- subject(s): Numbers, Prime, Prime Numbers, Sieves (Mathematics)
State the characterictics prime numbers share?
The crucial importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic.
How many prime number exist in mathematics?
I am sure that there are 25 prime numbers exist in mathematics
What was the contribution of euclid in number system?
Euclid contributed to number theory, which is the study of integers. He worked on prime numbers and divisibility. He proved the infinitude of prime numbers, which had not been proven before.
Who are euclids parents?
eetrgrv
How is the number theory different from arithmetic?
Arithmetic can be written as two different products of prime numbers. haha
What do numbers are relatively prime?
In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime (also spelled co-prime) if the only positive integer that evenly divides both of them is 1. That is, the only common positive factor of the two numbers is 1.
Number theory is the queen of mathematics?
This is told by Carl F. Gauss: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." There are different types of numbers: prime numbers, composite numbers, real numbers, rational numbers, irrational numbers and so on. This study of numbers is included within the concept of maths and numbers and it is very important a study. Therefor number theory holds a greater importance too.
What has the author Edgar Dehn written?
Edgar Dehn has written: 'Algebraic equations' -- subject(s): Dynamics, Galois theory, Group theory, Lagrange equations, Theory of Equations 'Prime numbers'
What number is relatively prime?
In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime (also spelled co-prime) if the only positive integer that evenly divides both of them is 1. That is, the only common positive factor of the two numbers is 1.
