How to increase precision in this case?

I have a code which finds the first 10 consecutive numbers after decimal that forms a prime number:

k = 10;

while true

a = mod(floor((pi-3)*10^k),10^10);

if isprime(a) == 1

disp(a)

break

endif

k += 1;

endwhile

And this only works for pi, I also need it to e but its not enough precision

What can i do here?

Answer 1

[John D'Errico]

Take it from here:

vpa(exp(sym(1)),500)

ans = 

2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920695517027618386062613313845830007520449338265602976067371132007093287091274437470472306969772093101416928368190255151086574637721112523897844250569536967707854499699679468644549059879316368892300987931

Now just process the digits.

Or I think I have something on the order of a million digits of e and pi stored in my HPF toolbox. (Might be only a half million.)

[Daniel]

But if i do so and run the same code, 'a' stucks at this:

[Daniel]

Help me pls John. Idk what to do here. Im sitting with this stupid problem for 3 hours

[John D'Errico]

Can you extract the string of digits? I think you are fixated on the idea that you NEED to work with numbers, and there is only one possible way to extract those digits. That is completely wrong. I showed you how to extract all the digits you want. Perhaps I stopped one step short, thinking you could take it from there. So I'll add a next step.

D = char(vpa(exp(sym(1)),500))

D = '2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920695517027618386062613313845830007520449338265602976067371132007093287091274437470472306969772093101416928368190255151086574637721112523897844250569536967707854499699679468644549059879316368892300987931'

That is not a string of numeric digits there, but a string of characters. But even so, it is all you need. Feel free to delete the decimal point even.

D(2) = []

D = '27182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920695517027618386062613313845830007520449338265602976067371132007093287091274437470472306969772093101416928368190255151086574637721112523897844250569536967707854499699679468644549059879316368892300987931'

You can even convert them into actual numeric digits if you feel the need, but you need to make some effort, and I'm sorry, but I won't do your homework, and I've already done almost all of it here.

[Daniel]

Thank you John. We learned only loops (for, while) on the last lesson. I didnt know about it