Why is 2 ^2017 a math error

Sir-Emo is right    

 

This is how you can do it on any scientific calculator  

 

$$\\y=2 ^{2017}\\ logy=log2 ^{2017}\\ logy=2017*log2\\$$

 

$${\mathtt{2\,017}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{2}}\right) = {\mathtt{607.177\: \!501\: \!254\: \!250\: \!080\: \!4}}$$

 

$$\\logy=607.1775012542500808\\\\ y=10^{607.1775012542500808}\\\\ y=10^{0.1775012542500808}\times 10^{607}\\\\$$

 

$${{\mathtt{10}}}^{{\mathtt{0.177\: \!501\: \!254\: \!250\: \!080\: \!8}}} = {\mathtt{1.504\: \!877\: \!864\: \!909\: \!905\: \!7}}$$

 

$$2^{2017}=1.5048778649099057\times 10^{607}$$

Because this goes beyond the workable limit of most calculators.

This is because of the limitations of the computer system: they can only store numbers up to a certain size and to do this equation it needs to FAR exceed this.

 

To put it simply: computers of a "32-bit" system can use numbers that take up 32 bits of space, i.e. have 2³² different numbers (inluding 0). "64-bit" are similiar but can do up tp 2⁶⁴.

No current operating system in the world will support what you are asking for in integers.

 

However, there is a way to calculate this using things called "longs" (Numbers with no limited bit-length). The issue here is calculators will virtually never use these for efficiency reasons.

I quickly made myself a program to do this, and the output is:

 

1504877864909870890002459133447611330097732258481694573170055888012268354132207

6177782007219047710981075054947716136472064126077643824238840065967471547556631

5608459372543711642502796605181191613879323184416012690760159020510594156393027

3723717600594767445970887146193668599049166825870452800411690209544520914290723

8410945246315083832742911528263323025464230244084170860858180649908473861473732

9040021529033435245993167449987296007346139762764351459674598804149922109794266

1066549351679026229629820374291322314211013630733173213356779824859254302754506

3446994685630981451647656652367955517092809805578371072

 

In scientific notation that is about: 1.5049 * 10⁶⁰⁷

yeh...That's kinda big