Timeline for Mid-Square with all bits set
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2022 at 18:58 | vote | accept | bobuhito | ||
| Mar 14, 2022 at 18:40 | comment | added | fgrieu | Problem (as stated) solved!. Perhaps the question needs to be re-generalized. | |
| Mar 13, 2022 at 16:44 | answer | added | fgrieu | timeline score: 7 | |
| Jan 17, 2017 at 16:11 | comment | added | Max Alekseyev | @GerhardPaseman: The confusion was that "128-bit" here does not refer to the size of computer arithmetics (in which a square would be 128-bit integer as well), but just to the size of an given integer while the arithmetics is done traditionally. | |
| Jan 17, 2017 at 15:56 | answer | added | Max Alekseyev | timeline score: 6 | |
| Jan 15, 2017 at 20:30 | comment | added | Gerhard Paseman | Oops. That's 2^64 - 1, not 2^32 - 1. Never mind. Gerhard "Anyone Got A Billion-core Multiprocessor?" Paseman, 2017.01.15. | |
| Jan 15, 2017 at 20:29 | comment | added | Kevin Buzzard | I think I need a loop of size $2^{64}$ (see my partial answer below). What am I missing? Can you explain more precisely? | |
| Jan 15, 2017 at 20:27 | answer | added | Kevin Buzzard | timeline score: 6 | |
| Jan 15, 2017 at 20:13 | comment | added | Gerhard Paseman | @Kevin, if you have the cluster to brute force a calculation involving 2^28 trials , this one can be resolved with little more. Just iterate through square roots of ta+d for t from 0 to 2^32 -1 and a and d appropriately chosen, and see which ones are close enough to integers. Gerhard "What's A Billion Between Processors?" Paseman, 2017.01.15. | |
| Jan 15, 2017 at 20:02 | comment | added | Gerhard Paseman | @Max, in many implementations often the 192d bit of a 128 bit integer is 0, although it can be undefined. What is requested is a consecutive swath of bits from the square of a 128 bit integer, which seems interesting when the integer is appropriately large. Gerhard "Will Try Some Short Cases" Paseman, 2017.01.15. | |
| Jan 15, 2017 at 19:37 | history | edited | GH from MO |
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| Jan 15, 2017 at 19:20 | comment | added | Max Alekseyev | What is 192nd bit of 128-bit integer? | |
| Jan 15, 2017 at 17:40 | comment | added | Kevin Buzzard | I don't see any way of answering this other than by a brute force computation (although some brute force methods are quicker than others). We can replace 128 by any even number 2m and the question still makes sense, and has a positive answer for 2m=8,10,20,22,24,26,28,...but negative answers for other even numbers <= 28. The calculation will take too long (for me) for 128 and the question just seems like an idle one to me so I don't think I'll be using the work cluster to investigate it... | |
| Jan 15, 2017 at 17:10 | comment | added | bobuhito | Smaller numbers are fine. Any of the 128 bits can be zero. | |
| Jan 15, 2017 at 17:07 | comment | added | Kevin Buzzard | Is a 128-bit integer necessarily at least $2^{127}$? (or can the first few bits be zero?) | |
| Jan 15, 2017 at 16:56 | comment | added | Boris Bukh | Sure, any number <2^32 has the property you wish. | |
| Jan 15, 2017 at 16:37 | comment | added | bobuhito | It's simplified from math.stackexchange.com/questions/2096308/… and crypto.stackexchange.com/questions/42923/… | |
| Jan 15, 2017 at 16:35 | comment | added | Wojowu | May I ask why you are interested in this question? | |
| Jan 15, 2017 at 16:32 | history | asked | bobuhito | CC BY-SA 3.0 |