@Carl Love 
Thanks

I am looking to the upgrade of the AMD ryzen 6 core processing and further i found..

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AMD Ryzen 5 1600 offers 9% more performance per watt. Specifications: The AMD Ryzen 5 1600 has a thermal design power (TDP) of 65 Watts; The Intel Core i7-6850K, Intel’s lowest-power 6-core processor, has a thermal design power (TDP) of 140 Watts. Performance may vary based on use of latest drivers. RZN-37
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That TDP of 65 Watts is really good for the energyconsumption and reliability of the computerssytem..too much heath is a problem for the electronics as i know from my own experience.

@janhardo 

CPU and internal memory are important for computer speed, and it seems that the SDD only is for starting up the system as i have informed at the computerstore.

@janhardo 

Well,were is the next prime is be answered in this article : Where is the next Mersenne prime? (utm.edu)
Some statistics used to predict the gap between the known 51 mersenne prime and the following unknown 52 mersenne prime 
This 52 mersenne prime quess can be a prime or not  

Quote :
So what can we gather from this?  One thing is that given one Mersenne prime exponent's p, the next one will fall, on the average, near 1.47576p.  But not too near the average much of the time--sometimes the gaps will be small, sometimes large.  So the next larger Mersenne exponent might be over 85,000,000 yielding a Mersenne with nearly 26 million digits.  Or it may not.

Mersenne prime 51 = 82,589,933 x 1,47576 = 121.882.919,5 (mersenne prime 52 expected on average 
But is it not that the gaps between mersenneprimes becomes larger and larger direction infinity, but we are now here on mersenne prime of p= 85 million to start with the search 
Don't know how they it doing on the GIMPS website with there search?

@Carl Love 

Looks like the internal computer memory is not a bottle neck for speed, so a fastest SDD drive on a motherboard can increase speed of calculations.
Wonder if the search to a bigger prime is not done by a supercomputer ?

12 Fastest Supercomputers In The World | In 2021 - RankRed

How do they do it on the GIMPS website ?

@janhardo 

A external sdd drive is  plug and play goes to 2000 Mb/s for reading /writing for all models
The motherboard ssd's  are much faster and cheaper but must be built in, but it is not big deal

@acer 

Thanks

Probably i change  something in the  Tools->Options->Display 
Its now working again.

@janhardo 

Can i go reverse ..and  express 10^ 24,862,048 as mersenne exponent prime ?
1,39822 x 10^316 could be  a mersenne prime or not ? 
In general ,how to search from the latest found primenumber further: what number to take as next one ?
Mp = 2^(last one +1) - 1 ..no estimation for this ?

The next Mersenne prime will be about 2x times bigger then his precessor
example : 2^4 ( forget this -1)  =   2^3 -1 x 2^1 , but calcualtion time is not doubling as  two calculation has shown for two mersenne primes and it doesn't matter for CPU speed, i think, it all goes now faster with the same speed ratio's in time.
Its a exponential curve 2^x ..

@Carl Love 

Thanks

So, the latest biggest found primenumber can be expressed as 

 10^ 24,862,048
Its lot bigger then number of atoms in our universe 10^80 

@tomleslie 
Thanks,

I do get no plot, but this..
`Standard Worksheet Interface, Maple 2021.1, Windows 10, May 19 2021 Build ID 1\
539851`
INTERFACE_PLOT(CURVES(Matrix(932,2,{(1, 1) = HFloat(1.), (2, 1) = HFloat(3.6235\
4490699999987), (2, 2) = HFloat(2.), (3, 1) = HFloat(5.90627730299999953), (3,  ..and so on.

@janhardo 
The primecount function and his two approximations graph ..

• John E.Littlewood shows in 1914 that there are  infinity intersections with the two aproximations graphs and prime count graph. 
   
• Stanley Skewes claims that first intersection point is on x= 10^(10^10^34)
• Carter Bays &Richard Hudson claiming in 2000 that first intersection lies before
  number 1,39822 x 10^316 ( 10^80 atoms in universe) 

Problem is now how to find this intersection point with computer and how far is this from the last found  Merssene exponent  prime number?

@Ronan 

Thanks,
Memorize some basic examples will help.

@Carl Love 

Thanks!

With this i can express a Mersenne prime number as number with base 10^MersenneDigits 

@tomleslie 
Thanks,

Yes, amazing comparison.

It are big numbers, but compared with infinity ?
Distribution graph of Mersenne Primes found by GIMPS,can give perhaps a direction for the search interval for the next new Mersenne prime ?
List of known Mersenne prime numbers - PrimeNet

You know the number on numberline from the latest Mersenne prime found in comparison with a 1000 number segment : position ?

Is there a faster algorithm to find for calculating the number of primes given to a certain number ?

@janhardo 
Impact has also the used SDD on the calculation speed : read 560 Mb/s and write 510 Mb/s is now used on my computer.
There are two slots on motherboard for M.2-sdd and  using a read 3500 Mb/s and write 2300 Mb/s sdd can make a difference?
Using IOPS as number of read/write performance..
IOPS read 360.000 and write : 390.000 as example here ( WD blue for 60 USD) ( see here the kingston fury(new) m.2-sdd 4 TB  : cost more then 1000 USD and 1,000,000 IOPS read /write) 
The cheapest way for now to get performance improvement is upgrading to a faster M.2-sdd
Maple must be then be installed on this faster SDD. 

Corsair MP600 PRO XT, 4 TB SSD Zwart, CSSD-F4000GBMP600PXT, M.2 2280, PCIe 4.0 x4 (alternate.nl)
A PCIe Gen4 x4 controller for exceptional data performance delivers phenomenal read, write and response speeds that make standard M.2 SSDs pale in comparison.

Well, using asus fast(est) gaming motherboard and a amd fast cpu  and fast sdd and fast memory can give a improvement for the Mersenn prime calculation.
Now i know why it take so much time to discover a new biggest unknown primenumber and knowing where to start for searching for sure ( gap estimation ) ? 
 

@mmcdara Thanks! There is a procedure what can calculate the latest known Mersenne prime, although it takes some time. I did calculate Mersenne prime _number 40 and it took roughly 7,5 hour ( i must check this ). Dividing the numberline  in 1000 number sections to the latest known mersenne prime is also probably impossible, because the number is very big. At the moment i am trying to express this latest mersenn prime number in a power of 10 ?