2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149
That's an infinite list.
The set of primes would be one. The set of Mersenne primes is another. The set of all primes below 50 is another. And so on. A set which includes all primes, and only them, is the set of numbers having exactly 2 factors.
There are infinitely many numbers, and these comprise infinitely many primes and composites. It is not possible to list them all.
Euclid's proof that there are infinitely many prime numbers is based on contradiction. He starts by assuming there is a finite list of primes, ( p_1, p_2, \ldots, p_n ). He then considers the number ( P ) formed by multiplying all the primes in the list and adding one: ( P = p_1 \times p_2 \times \ldots \times p_n + 1 ). This number ( P ) is either prime itself or not divisible by any of the primes in the original list, thus proving that there must be at least one more prime not in the list, contradicting the assumption of finiteness.
NO because there is an infinite number of them, just like there is an infinite number of primes. In fact, if there is an infinite number of primes there must be an infinite number of composite numbers too... do you see why?
There are infinitely many primes so it is not possible to list them all. Moreover, there is no simple rule that can be used to describe a list of all primes.
That's an infinite list.
That's an infinite list.
There are an infinite amount of non primes (and primes). It would be impossible to list them.
Euclid proved there are infinite. He said that if there were a finite number of primes, if you multiply all the primes together and then add 1, the result will be a prime. Thus, there are infinite primes.
The set of primes would be one. The set of Mersenne primes is another. The set of all primes below 50 is another. And so on. A set which includes all primes, and only them, is the set of numbers having exactly 2 factors.
There are infinitely many numbers, and these comprise infinitely many primes and composites. It is not possible to list them all.
Euclid's proof that there are infinitely many prime numbers is based on contradiction. He starts by assuming there is a finite list of primes, ( p_1, p_2, \ldots, p_n ). He then considers the number ( P ) formed by multiplying all the primes in the list and adding one: ( P = p_1 \times p_2 \times \ldots \times p_n + 1 ). This number ( P ) is either prime itself or not divisible by any of the primes in the original list, thus proving that there must be at least one more prime not in the list, contradicting the assumption of finiteness.
NO because there is an infinite number of them, just like there is an infinite number of primes. In fact, if there is an infinite number of primes there must be an infinite number of composite numbers too... do you see why?
here are all 8, 3,5 11,13 17,19 59,61 29,31 41,43 5,7 71,73
All Factors of 150:1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Vermont has 150 members of the House, but only thirty State Senators.