2007-03-21 17:46:15 · 7 answers · asked by grm20764 1 in Science & Mathematics ➔ Mathematics
I think not.
A prime number is a positive number with exactly 2 factors: 1 and itself. Natural numbers are only positive.
The number 1 is not prime, as it only has 1 factor. This makes 2 the first prime number.
Clearly, all multiples of 2 cannot be prime. Using the Sieve of Eratosthenes, you can easily show that there cannot be three consecutive numbers that are prime. To do the Sieve, list the numbers from 1 to x, where x is as big as you'd like (choose something reasonable). Cross out 1, as it cannot be prime. The next number not crossed out is 2. As mentioned, that is the first prime number. Cross out all multiples of 2 (hence, choosing a reasonable number for x). Go to the next number that is not crossed out, which is 3. This is the second prime. Cross out all multiples of 3 (i.e. 6 and 12 are already crossed out, but you can now cross out 9 and then 15, etc). The next prime is 5. You can quickly see that, since multiples of 2 are between any candidates for prime numbers, more than two consecutive primes (i.e. 2 and 3) are impossible.
2007-03-21 18:07:11 · answer #1 · answered by T 3 · 1⤊ 0⤋
There cannot be, because every even number greater than 2 is prime, and between two consecutive odd numbers there is an even number. That's an informal proof right here.
1 is a number that is considered neither prime nor composite, so 1, 2, 3 wouldn't be an example.
2007-03-21 17:49:03 · answer #2 · answered by Puggy 7 · 1⤊ 2⤋
no. if you have 3 consecutive natural numbers then 2 must divide at least one of them. the only time it might happen is 1, 2, 3. But technically 1 isn't prime nor is it composite (opposite of prime).
2007-03-21 17:58:35 · answer #3 · answered by JizZ E. Jizzy 2 · 2⤊ 0⤋
No there can't be. this is because of fact if the three numbers have been to be consecutive then one in all them might might desire to a good form. as such it does not be a primary because it is likewise divisible by using 2. regrettably the sole 3 that could have been (a million,2 and 3) are disqualified rationalization for a million. its not a primary. i think of.
2016-11-27 21:23:28 · answer #4 · answered by ? 4 · 0⤊ 0⤋
Apart from 1, 2, and 3, the answer in - No.
Every number from 4 upwards is an even number, therefore it cannot be a prime because it is divisible by '2'.
2007-03-21 17:50:59 · answer #5 · answered by Just Helping 4 · 0⤊ 2⤋
1 2 3 are all primes, and all consecutive
2007-03-21 17:48:46 · answer #6 · answered by Archangel 4 · 0⤊ 4⤋
1,2,3 or -1, -2, -3
2007-03-21 17:49:21 · answer #7 · answered by misoma5 7 · 0⤊ 2⤋