No Twin Primes of Form 8p+1, 8p+1
\[8p-1, \; 8p+1\]
where \[p\]
is a prime number. To show this let \[p=3\]
then \[8p-1=8 \times 3-1=23, \; 8p+1= 8 \times 3+1=25=5 \times 5\]
.If
\[p=3k+1\]
then\[8p-1 = 8 \times (3k+1)-1=24k-7\]
.\[8p+1= 8 \times (3k+1)+1=24k+9=3(8k+3) \]
.If
\[p=3k+2\]
then\[8p-1=8 \times (3k+2)-1=24k+15=3(8k+5)\]
\[8p+1= 8 \times (3k+2)+1=24k+17\]
.Hence there are no twin primes of this form.
