- #1
Math100
- 768
- 219
- Homework Statement
- Verify that the integers 1949 and 1951 are twin primes.
- Relevant Equations
- None.
Proof:
Consider all primes ## p\leq \sqrt{1949} \leq 43 ## and ## q\leq \sqrt{1951} \leq 43 ##.
Then we have ## p\nmid 1949 ## and ## q\nmid 1951 ## for all ## p\leq 43 ##.
Thus, ## 1949 ## and ## 1951 ## are both primes.
By definition, twin primes are two prime numbers whose difference is ## 2 ##.
Note that ## 1951-1949=2 ##.
Therefore, the integers ## 1949 ## and ## 1951 ## are twin primes.
Consider all primes ## p\leq \sqrt{1949} \leq 43 ## and ## q\leq \sqrt{1951} \leq 43 ##.
Then we have ## p\nmid 1949 ## and ## q\nmid 1951 ## for all ## p\leq 43 ##.
Thus, ## 1949 ## and ## 1951 ## are both primes.
By definition, twin primes are two prime numbers whose difference is ## 2 ##.
Note that ## 1951-1949=2 ##.
Therefore, the integers ## 1949 ## and ## 1951 ## are twin primes.