In the isolated islands of function thread, Origenes cited the exact value of one of a big number. GP asked, how did you do it, as Excel and R are overwhelmed at that sort of level.

Origenes answered:

Origenes, 104: >> . . . I found this website: https://defuse.ca/big-number-calculator.htm >>

Now, I have routinely used logs and high-capacity hardware calculators [e.g. HP 50] or software ones [X-Calc and Emu-48], but obviously these give rounded answers.

I popped over to the linked page (now on speed dial, of course), and so — for reference:

KF, 106: >>2^500 =

3 273390 607 896 141 870 013 189 696 827 599 152 216 642 046 043 064 789 483 291 368 096 133 796 404 674 554 883 270 092 325 904 157 150 886 684 127 560 071 009 217 256 545 885 393 053 328 527 589 3762^1000 =

10 715086 071 862 673 209 484 250 490 600 018 105 614 048 117 055 336 074 437 503 883 703 510 511 249 361 224 931 983 788 156 958 581 275 946 729 175 531 468 251 871 452 856 923 140 435 984 577 574 698 574 803 934 567 774 824 230 985 421 074 605 062 371 141 877 954 182 153 046 474 983 581 941 267 398 767 559 165 543 946 077 062 914 571 196 477 686 542 167 660 429 831 652 624 386 837 205 668 069 376That will help those who have problems with rounded values, such as 3.27*10^150 and 1.07*10^301. Though, the rounded values give the order of magnitude with a lot more clarity.

While I am at it, let’s look at the doubling effect of doing 2^1001:

2^1001 =

21 430172 143 725 346 418 968 500 981 200 036 211 228 096 234 110 672 148 875 007 767 407 021 022 498 722 449 863 967 576 313 917 162 551 893 458 351 062 936 503 742 905 713 846 280 871 969 155 149 397 149 607 869 135 549 648 461 970 842 149 210 124 742 283 755 908 364 306 092 949 967 163 882 534 797 535 118 331 087 892 154 125 829 142 392 955 373 084 335 320 859 663 305 248 773 674 411 336 138 752That is, 2.14 * 10^301, pretty nearly.>>

Food for thought. **END**

Origines finds a handy “big number” calculator — some reference results for 2^500 and 2^1,000. KF

KF:

Thank you for headlining that. It’s really an useful resource.

And, of course, thank you to Origienes for finding it.

Do you know any PC software that can compute the rounded values and the math for very big numbers?

Both Excel and R seem to be limited at about 10^307, if I am not wrong. What I need is some software that can compute the values, in scientific notation, for much bigger numbers. Maybe it’s a limitation of the system (Windows)?

GP, I have emu48, which is a software emulator for the HP 48 calculator. I think this page should do it, but there may be hiccups: http://hp.giesselink.com/emu48.htm Warning, RPN logic, but then I have been HP since the HP 21. (I just bought the HP12 to replace my Victor V12 knockoff, I forgot I bought alkaline batteries and corroded terminals.) Maybe, just go hardware? KF

PS: There are emulators for TI calcs that may do much the same. XCalc is also good. I suggest, work with logs. There is a TI calc that is for heavy duty work that has emulation too, TI 92 is it? Yup, try: https://sourceforge.net/projects/gtktiemu/ Hardware is here: https://www.amazon.com/Texas-Instruments-TI-92-Graphing-Calculator/dp/B00000JBO3

PPS: Another online calculator: https://keisan.casio.com/calculator

KF:

Thank you!

I am doing some tests.

The Boost C++ library may be of interest: boost.org

There are a number of possible alternatives noted here:

https://en.m.wikipedia.org/wiki/List_of_arbitrary-precision_arithmetic_software

Looks like the ordinary Windows Calculator also has significant capability and a scientific mode: https://en.m.wikipedia.org/wiki/Windows_Calculator