202 = ( ( 4 + 4 ) / 4% ) + sqrt(4)
202 = 4 ^ 4 - ( 4! / .4~ )

203 = gamma(gamma(4)) / √.4~ + 4! - gamma(√4)
204 = (√4 / .4)! / √.4~ + 4!
205 = gamma(gamma(4)) / √.4~ + gamma(√4)
206 = gamma(gamma(4)) / √.4~ + √4

[QUOTE=Andi47;102007]203 = gamma(gamma(4)) / √.4~ + 4! - gamma(√4)
204 = (√4 / .4)! / √.4~ + 4!
205 = gamma(gamma(4)) / √.4~ + gamma(√4)
206 = gamma(gamma(4)) / √.4~ + √4[/QUOTE]

205 and 206 are presumably missing '+4!'

207 = (4! * gamma(4) - gamma(4)) / √.4~
208 = 4 ^ 4 - 4! - 4!

*grrrrrr*

catching two loose 4!'s:

205 = gamma(gamma(4)) / √.4~ + 4! + gamma(4)
206 = gamma(gamma(4)) / √.4~ + 4! + √4

moving on:
209 = ((gamma(4) + gamma(√(4)))! - 4!) / 4!
210 = (4! + 4! / .4) / .4
211 = (gamma(4 + 4) + 4!) / 4!
212 = 4 ^ 4 - 44

[QUOTE=cheesehead;101950]... and now one of those exciting prime decades!

191 = ((gamma(4))! + 44) / 4
192 = (44 + 4) * 4[/QUOTE]


May I suggest you start a new thread "Cheesehead prime four" with your rules. Pleasde note that GAMMA IS NOT IN THE ORIGINAL RULES!

[QUOTE=Wacky;101833]Most of us are not interested in your "change of the rules". If you are allowed to change the rules to suit yourself, then any value becomes trivial.

Please stick to the established restrictions.[/QUOTE]


Does the useof gamma and % make all numbers trivial?

[QUOTE=PrimeCrazzy;102075]May I suggest you start a new thread "Cheesehead prime four" with your rules. Pleasde note that GAMMA IS NOT IN THE ORIGINAL RULES![/QUOTE]
No, it isn't; but surely the fact that gamma (and per cent) has been used by several others as well as Cheesehead suggests that there may have been an amendment to the rules. If you go and read post 104 in this thread, the person who started this thread clearly says;
[QUOTE=petrw1;99011]...fo(u)r the sake of progress I'm game with allowing % and gamma. And I like [Andi47's] recommendation that the preference is to NOT use them and solutions without them will replace solutions with them.[/QUOTE]
So, in order that the continuation of consecutive numbers being solved does not get bogged down, the person who set up the thread has decided to allow gamma and per cent, although gamma-less and per-cent-less solutions found for lower numbers will supercede the earlier solutions.
The key difference is that gamma and per cent were deemed acceptable only when a point was reached where a number was apparently unobtainable using the initial functions. Sum and subfactorial, on the other hand, were put forward when not strictly necessary by someone who had clearly not bothered to read the thread properly. Looked at in this strictly logical manner, I think it's understandable why Cheesehead may have been a little impatient with you.
Now, if you'd like to join in on this puzzle [1] using the rules so far established I'm sure no-one would object. If you would like to start a new thread using sum and subfactorial, but neither gamma nor per cent, then by all means do so - although, I recommend choosing a different set of numbers as well otherwise people may be discouraged from taking part in something which is very similar to an existing active thread.
Either way, calm down, take a deep breath, and relax.

[1] Is this thread a puzzle or a problem? Is there a technical difference between the two?

[quote=PrimeCrazzy;102075]May I suggest you start a new thread "Cheesehead prime four" with your rules. Pleasde note that GAMMA IS NOT IN THE ORIGINAL RULES![/quote]I wanted to facilitate progress of the thread to higher numbers, without using any operator (such as %)[sup]*[/sup] to which I object more strongly than to the gamma. I didn't propose, introduce, or approve the gamma function here. I had previously stated my preference not to extend the allowed operators, and didn't want to repeat that. Also, I admired the simplicity of the 192 solution, and wanted to be the one to post it.

In view of my earlier objections, [I]it would have been a good idea for me to have stated my motivations[/I] in order to ward off misunderstanding. I apologize for omitting that.

I was not irritated by your suggestions to add sum and subfactorial. My post #124 suggestion about starting a new thread was punctuated with a :smile: to signal that it was intended as a friendly, not hostile, suggestion about how to achieve what you wanted without further modifying the present thread. I wrote "... those of us interested in that set ..." because I was (and still am) genuinely interested in participating in such a thread, but I didn't state my interest explicitly. I wouldn't object to using either the sum or subfactorial if the thread originator specified them. I'd simply avoid participating if I objected to the originator's set of rules in that context.

- - - - -

[sup]*[/sup] I previously objected to % and decimal point equally. I've changed my opinion since then, to accept decimal point (implied division by 10, if followed by a single-digit number) more readily than percent (implied division by 10[sup]2[/sup]).

213 = (gamma(gamma(4)) + 4! - √4) / √.4~
214 = 4 * 4! / .4~ - √4
215 = 4 * 4! / .4~ - gamma(√4)
216 = 4! * (4 + 4) + 4!

[QUOTE=DJones;102163]
215 = 4 * 4! / .4~ - gamma(√4)[/QUOTE]

215 = ((4 * 4!) - .4~) / .4~

217 = (4 * 4! + .4~) / .4~
218 = 4 * 4! / .4~ + √4
219 = (4! * gamma(4) + √4) / √.4~
220 = 4 * 4! / .4~ + 4

[quote=DJones;102163]213 = (gamma(gamma(4)) + 4! - √4) / √.4~[/quote]With single gamma:

213 = (4! * gamma(4) - √4) / √.4~