The number 2^3217 -1 is a very large prime find how many digits it would take to write the number in decimal form. ( Hint: Log 2 is an interesting irrational number It's the power of 10 that gives 2, in the same way, that 3 is the power of 10 that gives 100. Your calculator can calculate log 2)

Hans007
Feb 9, 2018

#1**+2 **

The number is a very large prime find how many digits it would take to write the number in decimal form. ( Hint: Log 2 is an interesting irrational number It's the power of 10 that gives 2, in the same way, that 3 is the power of 10 that gives 100. Your calculator can calculate log 2)

\(let \\\;\;y=2^{3217} \\ log(y)=log(2^{3217} )\\ log(y)=3217\;log(2 )\\ log(y)\approx3217*0.301029995\\ log(y)\approx\;968.4134961\\ 10^{log(y)}\approx\;10^{968.4134961}\\ 10^{log(y)}\approx\;10^{0.4134961}*10^{968}\\ y\approx\;2.59*10^{968}\\ 2^{3217}\approx\;2.59*10^{968}\\ 2^{3217}-1\approx\;2.59*10^{968}\\\)

This is an integer, so the number is 2 followed by 968 more digits.

**So the the number is 969 digits long**

Melody
Feb 9, 2018