20210530, 18:17  #1 
May 2018
233 Posts 
2^64 is not a big number!
We have searched all primes up to 2^{64}=18446744073709551616, but that is not a big number. If something had 2^{64} atoms in it, then it would be like a small grain of sand. 2^{64} is a small number when it comes to atoms.

20210530, 19:32  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
25314_{8} Posts 
Quote:
Easily visible but not especially large  about 1mm across. 

20210530, 19:52  #3 
Jun 2015
Vallejo, CA/.
3×337 Posts 
Bobby: There is very little correlation between small numbers in the Physical world and "small numbers" when it comes to searching for primes.
PRIMO has the capability of proving primes in the range of 10^{40000} to 10^{50000} LucasLehmer can prove Mersenne primes in the order of 2^{100,000,000} to probably 2^{1000,000,000} (with current technolog). In the physical world Atoms in the planet Earth. (approx) 10^{52} Atoms in the Solar System (if it is conceived as a solid sphere of 50 Light Year Radius is of the order of 10^{69} Even if you go the atoms in all know Undiverse which is estimated to have Radius of 4.65*10^{10} lightyears, the number of atoms in that volume would "only be" 2*10^{106} So, in conclusion even a number as "small" as 10^{120} would have no equivalent in the physical world. You can try creating sort of fancy artificial numbers: for instance the number of distinct molecules theoretically possible by combining up to 1000 atoms of Carbon, Oxygen, Nitrogen, Hydrogen, Chlorine, Magnesium, Iron, Flour, Calcium and Sodium atoms but even that won't get you any closer the the smallest composite number that has not been factored which is RSA260 (Of course they are millions of smaller numbers that have not been factored, but that is because no serious effort has been applied to them.) Last fiddled with by rudy235 on 20210530 at 20:04 
20210530, 20:08  #4  
Apr 2020
2·251 Posts 
Quote:
Quote:


20210530, 23:08  #5  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
2^{4}·191 Posts 
Quote:


20210531, 00:25  #6 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·7·449 Posts 
I've seen estimates of the total number of configurations (permutations or orderings?) of all particles in the observable universe is ~10^360.
What about TREE(3)? Or TREE(G)? Or TREE(G)^^...^^TREE(G)? What do you compare it to? Compared to infinity, all numbers you can think of will be insignificant and lost in the rounding error. 
20210531, 02:23  #7 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
2^{4}×191 Posts 

20210531, 04:02  #8 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3^{2}×239 Posts 
If you started drawing 10 short lines/notches every second 24/7, it would take you well over 7 billion years to finish drawing 2^64 lines.
Light travels 0.3 Micrometers (1/1000 of a millimeter) in 1 femtosecond. Light will travel more than 18446 LightYears in 2^64 femtoseconds. This is more than 4000 times the distance to the closest stars to our sun. ETA OTOH, If you could fold a piece of paper (in half) a mere 64 times it would have 2^64 layers. The SamuraiSwords (as well as the ChineseNoodles) are folded about 50 times and stretched/flattened each time. This gives the sword an edge which is about one molecule thick. Last fiddled with by a1call on 20210531 at 04:17 
20210601, 04:18  #9  
May 2007
Kansas; USA
10522_{10} Posts 
Quote:
2^64 = 18,446,744,073,709,551,616 (~1.8447 * 10^19) 2^64 / 3600 seconds per hour / 24 hour per day / ~365.25 days per year / = ~584,542,046,090.6 years. At 10 lines / second it would be 1/10th that length but would still be ~58,454,204,609.06 or ~58.454 billion years! Since 10 lines per second seems a little faster than the average person can write...I would go with 1 line per second, which would take ~584.542 billion years!! Either way it's likely longer than the universe has been around. Last fiddled with by gd_barnes on 20210601 at 04:23 

20210601, 11:47  #10  
Aug 2002
2×3×5×277 Posts 
Quote:


20210601, 12:57  #11 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}×3×11×83 Posts 
I'd like to see you walk from the Earth to the Moon.

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Finding multiples of a real number that are close to a whole number  mickfrancis  Math  16  20170301 07:17 
Estimating the number of primes in a partiallyfactored number  CRGreathouse  Probability & Probabilistic Number Theory  15  20140813 18:46 
Number of distinct prime factors of a Double Mersenne number  aketilander  Operazione Doppi Mersennes  1  20121109 21:16 
Estimating the number of prime factors a number has  henryzz  Math  7  20120523 01:13 
Fermat number F6=18446744073709551617 is a composite number. Proof.  literka  Factoring  5  20120130 12:28 