1)
I know four Prime numbers from Pi without point.
Do you know more?
2) How we can find this numbers not manual - by programming?
3) It the problem correct and solved?
Your last number is only correct if you use rounded numbers. The last 9 is not a digit of pi.
I guess Mathcads symbolics will not allow us to find more of that kind of numbers. The float command is limited to 250 significant digits (which also means that I should have used 249 instead of 251 😉
You'll have to use a more capable program for further investigation, maybe good old Derive could be of help as there the number of digits is limited only by available memory (but being rather old I suspect it will not be able to use more than 1 GB). How about the abilities of Maple?
Remark: As Stuart has show with his attempts below, those routines will only provide numeric IEEE precision. So only numbers up to 15 significant digits can be found, no matter how large s is chosen.
While the new symbolic engine allows values larger than 250 in the "float" modifier, it fails in the program if "s" exceeds 20 😞
The error message is "Unknown error: Integer_expected"
If you need an Express prime generator good for about 1000 primes (primes up to 8999), perhaps the following may be of service ...
The "module" is standalone in the sense that you can just copy the whole text region and paste it into a worksheet (taking care to avoid any name clashes).
Cheers,
Stuart
I just gave it a quick try and the symbolic evaluation of routines like your "pi_gen" fail because of the use of the "if" command in "head" and "tail".
Redefining p12list:=p12list= and then using the built-in Is Prime works OK, but of course the redefinition (actually already the conversion of the string to the number) limits us to the IEEE precision of the numerics.
The main problem is that "str2num" is a numeric only function and cannot be evaluated symbolically. So we are limited to 15 digits.
Thanks, Werner. Have you tried replacing the string conversions with a multiplication? For example,
where
piGen is unchanged but should return a numeric vector.
Cheers,
Stuart
@Werner_E wrote:
Not sure what you mean. Your pi_gen' still uses conditional expressions which can't be evaluated symbolically.
Hi Werner,
Having had a further look at my code, I suspect that the source of the problem is that IsEmpty tests for equality with nil, which just happens to be a single character. I'm guessing that this is the source of the conditional problem - I can't see how generic conditionals are going to create problems, but where there's a will there's a way.
I've poked around with my worksheet, replacing nil with some arbitrarily large negative integer (but one acceptable to the numeric processor), plus making a few other minor tweaks (eg, changing my IsPrime to prime?). I've added in some symbolic evaluations at appropriate points.
In addition, I've created a somewhat tidier, and more concise, worksheet that also adds a couple of programmed versions of Gosper's Spigot - one returns all members of the up-to-n-digits sequence, the other returns just prime members. Can't check on Express, of course, but, hopefully, they should be correct in principle (if not in typography!).
Cheers,
Stuart
Works like a charm 😉 Its OK with the old and with the new symbolic engine alike.
The code I posted in my first answer obviously is limited to numeric IEEE precision even though its evaluated symbolically. Otherwise this 38-digit number should have been in the result list.
I tried your routine up to 1000 and no additional prime was found. Not sure it thats true or if your program at some point has its limits concerning the number of digits used by the symbolics, too.
EDIT : The reason my routine does not work for higher numbers seems to be the symbolic evaluation of the "trunc" command as seen in the picture below. The new symbolic in Prime doesn't even know the trunc command.
Dear Mr. Werner_E, & All friends in Mathcad Prime.
Could you explain me, how to plotting array pile as show below picture to me please ?
Thank you all friends in advance.
From my future book!
Another mathematical problem that is also often used to compare computers and their software is finding large primes. This task is no longer empty fun - it has important practical applications in cryptography, for example. You can try to cross, as mathematicians put it, these two problems and find the maximum prime number of the form 314... Visitors to the site https://community.ptc.com/t5/PTC-Mathcad/Pi-and-Prime-numbers/td-p/677039 , on which the authors of this textbook posted this problem, found the first four primes forming the number π without a decimal point: 3, 31, 314159 and 31415926535897932384626433832795028841. In Figure an attempt was made to solve a modification of this problem: find the numbers π in the hidden “tail” (in the digital sequence following the well-known three digits 3.14).
The program in Figure, it was shown that within one hundred thousand characters of the number π in its "hidden" tail "there is only one prime number 104729 (3.141592653). And can you find an even greater prime number, if you go not up to a hundred thousand, but to a million, to a billion, a trillion, etc.? The question can be posed in another way: what is the largest prime number that can be found in the known set of found digits of π.
So, in the sequence of four million first digits of the number π (https://sanstv.ru/pi), the ten thousandth prime number 104729 (http://chemister.ru/Other/Text/primes10000.htm) is found only once. But there you can find another larger prime number 333667. This (the largest prime number in the sequence of digits of the number π) can be a new interesting task for testing both supercomputers and programmers who create programs for them.
Here is a replacement for "trunc" which works for higher numbers with the symbolics, too. Unlike "trunc" the routine "trunc2" has two arguments and works similar to "round" used with two arguments. The second argument is the number of decimals. I tried to create a real "trunc" replacement based on this routine, but I got the same faulty results as with the original "trunc".
But take care - "trunc2" IS FAULTY!!
If there are more than 10 nines after the last digit you want to see, it delivers a wrong result and there sure are positions in pi with more than 10 nines in a row! You can push this limit higher to 20 nines in a row, but there always will be a limit and so its not a reliable replacement.
I wasn't patient enough for the last expression to finish (the result 1 you see stem from copying and pasting the expression above and then changing the numbers. According to OEIS it should yield 1.
And if the "simple" evaluation of "IsPrime" takes so long, I guess the program with the for-loop will never in my life find that 16208-digit prime 😉
As Valery already said - its the wrong place here!
You asked the same question twice in midst of two threads which both have nothing to do with your question! Please avoid this for future questions.
To open a new thread with a question concerning Mathcad or Prime, go to
https://community.ptc.com/t5/PTC-Mathcad/bd-p/PTCMathcad
and then click "Start a topic".
Do you know the 3d Pi-Prime number? OSID does not know!
I know only than this number has more 1000 digits.
