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Comment Re:PGP signature (Score 1) 152

If you're not sure if you can trust the checksum, then how can you be sure you can trust that the presented public key is the legit one for the organization? Presumably you can get a trusted checksum from the publisher (like for Microsoft ISO's) and then verify the checksum matches the download you got from a somewhat sketchy source (like if you use a Torrent to download an OS ISO because your disc was damaged).

Comment Re:That's nothing (Score 1) 227

You're not missing it. 2 and 5 themselves (in decimal, or any base where they are factors of the base) are the only prime numbers ending in 2 and 5. So while GP is correct in a logical sense (there are at least a billion numbers afterwards ending in neither 2 nor 5 that are also prime) there are, in fact, infinite numbers afterwards ending in neither 2 nor 5.

This is not true in base-16 for 5's however (0x25 = 37 is prime for example), but remains true for 2's. It's completely false for base-7 though (base-7(32) = 23, base-7(25) = 19). So...yeah. I'll stop there. Further playing around with bases is left as an exercise to the reader.

Comment Re:What other bases does this hold for? (Score 3, Informative) 227

There are very few numerical properties that are base-dependent.

Some of the little tricks they teach you in school are strictly base-dependent, like if a decimal number ends in 5 or 0 it's divisible by 5 or 10 respectively. If a decimal number ends in a value divisible by 2 it's even else odd. Or if a decimal number's digits sum to a multiple of 3 or 9 then it's divisible by 3 or 9 respectively.

What they don't tell you is that is generalizable to other bases. Generically speaking if the final digit of a number in a given base is divisible by any factor of that base then the number itself is divisible by that factor (this should be fairly obvious) and if the digits of a number sum to a number divisible by a factor of (base-1) then that number itself is divisible by that factor (less obvious, but provable).

So for hex, for example, the factors of 16 are 2, 4, 8, 16. If a number in base-16 ends in 0 it's obviously divisible by 16, if it ends in 8 then it's divisible by 8 and so on. The factors of (16-1)=15 are 3, 5, and 15. So if the sum of digits of a hex number are divisible by 3, 5, or 15 then the number is also divisible by 3, 5, or 15 respectively as well.

Fun little math quirks on bases.

Comment Re:How about prime numbers of base 12 number? (Score 2) 227

The twin prime conjecture is independent of the base, so the base doesn't matter for it to be true or false.

I would find this surprising, since in a base 2 system every prime number ending in 1 is followed by a prime number ending in 1.

In base 2, every prime ending in 0 is also followed by a prime ending in 1.

Comment Latency? (Score 1) 172

I'm sure it's been considered but at least from a programming perspective I'd be more concerned about the latency on the port as regards the ability to process realtime high framerate graphics through there. When I was doing CUDA programming the most difficult (that is, time consuming) part was getting data from main memory to the graphics card. Would the Thunderbolt interface be as fast at shuttling data from main memory to an external graphics card? 40Gbps is great and all, but is the latency low enough?

Comment Re:Same goes for all other skills (Score 1) 908

Combinatorics is extraordinarily abstract. It's a senior level college math class at best, and I actually took a year of it in graduate school. I mean yeah, it's nice for explaining why the lottery is a scam, but it's very difficult for average folks to grasp. It doesn't feel intuitive at all.

Comment Re:This guy over here.... (Score 5, Informative) 254

The iPhone's flash drive is encrypted. The key is securely stored. If you guess the lock code incorrectly 10 times then it's not the hard drive that's erased, it's the key that is irrevocably destroyed. At that point it doesn't matter if you have a bunch of copies of the disk, you have a bunch of garbage and the only key in the universe was just wiped out.

Comment Re: Apple - standing alone (Score 1) 339

Ideally Apple will change this and allow an option to lock down recovery mode, maybe with the option of "if you forgot you pin, you can erase everything first," and refuse to load even signed software until the pin is entered or the device is erased.

My understanding is that they did change this in iPhone 5S and above models. The vulnerability only exists in this form on the 5C and regular 5 models. The terrorist's phone was specifically a 5C. The downside is if you comply with this order then it's possible to crack every single 5C out there with this method and that's a horrendous precedent to set.

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