The illustrated answer above is cool.
Here is something that might be quicker for you during an exam.
The prime numbers between $7$ and $150$ are all the neighbors of multiples of $6$, except:
- Those that end with $5$
- $49$
- $77$
- $91$
- $119$
- $121$
- $133$
- $143$
So you can simply:
- List all multiples of $6$
- List the two neighbors next to each one of them
- Memorize the ones mentioned above and eliminate them
UPDATE:
Just in order to clarify (and simplify) the method mentioned above.
All you have to do is to write down two lists, one starting from $7$ and the other starting from $11$.
Increment each list by $6$ until $150$, and eliminate the values that you have memorized in advance.
$\require{cancel}$
- $\small7,13,19,\color\red{\cancel{25}},31,37,43,\color\green{\cancel{49}},\color\red{\cancel{55}},61,67,73,79,\color\red{\cancel{85}},\color\green{\cancel{91}},97,103,109,\color\red{\cancel{115}},\color\green{\cancel{121}},127,\color\green{\cancel{133}},139,\color\red{\cancel{145}}$
- $\small11,17,23,29,\color\red{\cancel{35}},41,47,53,59,\color\red{\cancel{65}},71,\color\green{\cancel{77}},83,89,\color\red{\cancel{95}},101,107,113,\color\green{\cancel{119}},\color\red{\cancel{125}},131,137,\color\green{\cancel{143}},149$