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Twin primes are prime numbers with a difference of 2 e.g. 59, 61. There are no twin primes of the form  
\[8p-1, \; 8p+1\]
  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.