Question

Primes and are said to be twin primes if$q=p+2$ . For example, 3 and 5 are twin primes; so are 11 and 13. Find all pairs of positive twin primes less than 200.

Short answer

The required list of pairs is:

$$\begin{gathered} \left\{3,5\right\},\left\{5,7\right\},\left\{11,13\right\},\left\{17,19\right\},\left\{29,31\right\},\left\{41,43\right\},\left\{59,61\right\}, \\ \left\{71,73\right\},\left\{101,103\right\},\left\{107.109\right\},\left\{137,139\right\},\left\{149.151\right\}, \\ \left\{179,181\right\},\left\{191,193\right\},\left\{197,199\right\} \end{gathered}$$

Step-by-step solution

Write the prime number less than 200

Write the prime numbers that are less than 200.

$\left\{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199.\right\}$

Write all the pairs

Write the pairs in the form$\left(p,q\right)$ satisfyingthe condition $p+2$.

$\left\{3,5\right\},\left\{5,7\right\},\left\{11,13\right\},\left\{17,19\right\},\left\{29,31\right\},\left\{41,43\right\},\left\{59,61\right\},\left\{71,73\right\},\left\{101,103\right\},\left\{107.109\right\},\left\{137,139\right\},\left\{149.151\right\},\left\{179,181\right\},\left\{191,193\right\},\left\{197,199\right\}$

Thus, the required list is

$\left\{3,5\right\},\left\{5,7\right\},\left\{11,13\right\},\left\{17,19\right\},\left\{29,31\right\},\left\{41,43\right\},\left\{59,61\right\},\left\{71,73\right\},\left\{101,103\right\},\left\{107.109\right\},\left\{137,139\right\},\left\{149.151\right\},\left\{179,181\right\},\left\{191,193\right\},\left\{197,199\right\}$