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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.
What else can I help you with?
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 are similarities between prime numbers and prime colors?
Prime numbers and prime colors are both fundamental in their respective fields. Prime numbers are integers greater than 1 that are only divisible by 1 and themselves, while prime colors are pure and cannot be created by mixing other colors. Both prime numbers and prime colors are considered basic building blocks in mathematics and color theory, respectively. Additionally, just as prime numbers play a crucial role in number theory, prime colors are essential in fields such as art, design, and psychology.
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
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)
What are similarities between prime numbers and prime colors?
Prime numbers and prime colors are both fundamental in their respective fields. Prime numbers are integers greater than 1 that are only divisible by 1 and themselves, while prime colors are pure and cannot be created by mixing other colors. Both prime numbers and prime colors are considered basic building blocks in mathematics and color theory, respectively. Additionally, just as prime numbers play a crucial role in number theory, prime colors are essential in fields such as art, design, and psychology.
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.
What are numbers that have only two factors?
Numbers that have only two factors are called prime numbers. These numbers can only be divided by 1 and themselves without leaving a remainder. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. Prime numbers play a crucial role in number theory and cryptography due to their unique properties.
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
How many prime numbers between 1 and 8888888888888888888888888888888888888888888888?
To determine the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888, we can use the Prime Number Theorem. This theorem states that the density of prime numbers around a large number n is approximately 1/ln(n). Therefore, the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888 can be estimated by dividing ln(8888888888888888888888888888888888888888888888) by ln(2), which gives approximately 1.33 x 10^27 prime numbers.
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.
