no gamma, but with %:

157 = ((4% + √(.4~)) / .4~%) - √4

158 = √(√(√(4^4!))) / .4 - √4
159 = (√(√(√(4^4!)))-.4) / .4
160 = 4 * 4 * 4/.4
161 = (√(√(√(4^4!)))+.4) / .4

162 = (4 / .4~) ^ √4 * √4

[quote=petrw1;98449]how do you make 7 without using all the 4's?[/quote](4! + 4) / 4

petrw1, regarding your most recent "The list so far":

[quote]62 = (v4 / .4)! / (4 / v4)
62 = (v4 / .4)! / (4 / v4)[/quote]are identical mistakes -- both equal 60, rather than 62.

[quote]100 = 4!*4*(4/4)[/quote] = 96, not 100

[quote]137 = (4! /.4 ) / .4 + sqrt(4)[/quote]= 152, instead of 137.

Also, there are several duplications of correct formulas on successive lines. :-)

[quote=grandpascorpion;98488]160 = 4 * 4 * 4/.4[/quote]... or, to avoid any division, whether implied or explicit:

160 = 4^4 - 4!*4

[QUOTE=cheesehead;98561]petrw1, regarding your most recent "The list so far":

are identical mistakes -- both equal 60, rather than 62.

= 96, not 100

= 152, instead of 137.

Also, there are several duplications of correct formulas on successive lines. :-)[/QUOTE]

Guilty as charged....I will confess I took the answers so far on faith and merely merged them. I will double check them ... soon ....

[QUOTE=cheesehead;98560](4! + 4) / 4[/QUOTE]

So now if with only one more 4 we can square that 7 and make 8^2 or 64 we will have 113....hmmmmm

[QUOTE=petrw1;98569]So now if with only one more 4 we can square that 7 and make 8^2 or 64 we will have 113....hmmmmm[/QUOTE]

But that will be impossible. There is no way to create a square without consuming an additional 4. And we cannot generate 64 without using at least one (actually more) 4. Therefore the 7^2 + 64 approach will not work.

[QUOTE=Wacky;98601]But that will be impossible. There is no way to create a square without consuming an additional 4. And we cannot generate 64 without using at least one (actually more) 4. Therefore the 7^2 + 64 approach will not work.[/QUOTE]

Of course not ... that was just my feeble attempt at sarcastic humor.

Getting back on track ...
 

[quote=Andi47;98521]162 = (4 / .4~) ^ √4 * √4[/quote]163 = [I]another damn prime[/I]

Anyone?

- - -

And we don't have 157 within the OP's rules yet.