## Intervalo entre primos

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## Los números primos: parejas twin primes.

Sophie Germain primes are named after French mathematician Sophie Germain , who used them in her investigations of Fermat's Last Theorem.

It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven. It is conjectured that there are infinitely many Sophie Germain primes, but this has not been proven. A heuristic estimate for the number of Sophie Germain primes less than n is [11]. The form of this estimate is due to G. Littlewood , who applied a similar estimate to twin primes. Every term of such a sequence except the last is a Sophie Germain prime, and every term except the first is a safe prime.

Extending the conjecture that there exist infinitely many Sophie Germain primes, it has also been conjectured that arbitrarily long Cunningham chains exist, [13] although infinite chains are known to be impossible. Historically, this result of Leonhard Euler was the first known criterion for a Mersenne number with a prime index to be composite.

Safe and strong primes are useful as the factors of secret keys in the RSA cryptosystem , because they prevent the system being broken by certain factorization algorithms such as Pollard's rho algorithm that would apply to secret keys formed from non-strong primes.

Similar issues apply in other cryptosystems as well, including Diffie—Hellman key exchange and similar systems that depend on the security of the discrete log problem rather than on integer factorization. In the first version of the AKS primality test paper, a conjecture about Sophie Germain primes is used to lower the worst case complexity from O log 12 n to O log 6 n.

A later version of the paper is shown to have time complexity O log 7. Sophie Germain primes may be used in the generation of pseudo-random numbers. Note that these digits are not appropriate for cryptographic purposes, as the value of each can be derived from its predecessor in the digit-stream. Sophie Germain primes are mentioned in the stage play Proof [24] and the subsequent film. From Wikipedia, the free encyclopedia. Parts of this article those related to section, specifically the table need to be updated.

Please update this article to reflect recent events or newly available information. Are there infinitely many Sophie Germain primes? For details see Edwards, Harold M.

Retrieved 24 April Retrieved 18 April From The Prime Pages. November 22, , Are 'strong' primes needed for RSA? When Hal Harold remembers what a Germain prime is, he speaks to Catherine in a way that would be patronizing to another mathematician.

Eisenstein prime Gaussian prime. Pseudoprime Almost prime Semiprime Interprime. Probable prime Industrial-grade prime Illegal prime Formula for primes Prime gap. Retrieved from " https: Classes of prime numbers. Wikipedia articles in need of updating from January All Wikipedia articles in need of updating Articles containing potentially dated statements from March All articles containing potentially dated statements. Views Read Edit View history.

This page was last edited on 16 February , at By using this site, you agree to the Terms of Use and Privacy Policy. Unsolved problem in mathematics: List of prime numbers.

4out of 5dimaac–Keep working hard![CSVLB]damn bro i barely noticed you had a log goin on wtf lol. but anyways you look to be having the same progress as i did. definitely see change in the pics. great job at PRs too. looks like your having a smooth run good luck with the rest of cycle ill be checking in

5out of 5vilman–4. DB shrug: 60x3x10

3out of 5cfgth449–Diet: 207gP, 529gC, 86.5gF, 3725cal

4out of 5MAMOHCTPKuJI–Have a stock 1998 Cummins 24v dually with 38k miles. Been in the family since new, barely ever used after my dad got out of offroad racing.

5out of 5ghomm–rear delt machine 100xf 100xf 100xf

3out of 5Heliu–ahh well he definitely knows what he's doing when it comes to cutting![CSVLB]Aww thanks, unfortunately I was forced to have lots of practice cutting. I need ot get better at adding size lol!

3out of 5Tihan231–However, it may not have even been the tight and could have been the overindulgence in cardio . Cardio it seems can be quite addictive, but I still hate doing it.

3out of 5gregmanor2–I give it 10/10, even though damn is this stuff expensive. At $90 for 30 servings, that's $3 per serving. Even with how great this product is, I just can't justify spending that much, especially with just being out of college. If, however, you can afford it, then I'd recommend trying it. I'm going to try half the dose, so 2 capsules, and see how that works. That'd reduce the cost to $1.50 per serving, and a bottle would last a total of 12 weeks using it 5 days on and 2 days off. So overall, at 2 capsules per serving, it'd be roughly $1.07 per serving if averaged over 12 weeks.

3out of 5blabla9–I would like to drop another 10 lbs by the end of the, month, but I don't think that will happen.given that I go on vacation on July 27th.

4out of 5pepewka32–I'm exhausted. I really am taking the next couple of days off, because everything hurts, and I have no energy right now.[CSVLB]Short time today. Left with a decent pump. Didn't do a ton of work, but I was only in there for 45min, so not bad, and my back is feeling really tight and pumped. Pullups kind of felt like crap today and I had no endurance. Just hard to get focused.

3out of 5maleybest–5x prebed, gonna try it, reps[CSVLB]That's how I dose my I-GH-1; all 5 caps pre-bed. I groove on it. : That's the most beneficial time to take something like that. Only time I do it in the morning is if I'm on a fasted training routine.

3out of 5mav3r1ck–Will post an update shortly post-run!

4out of 5donyx–Was going good, finished workout quicker than usual with less rest between sets.

3out of 5sergio8–If I wanted to compete, would I have to be a member first?[CSVLB]K, thanks.

4out of 5munlana–I've been pumping an insane amount of old Thrice and Senses Fail recently, just feeling nostalgic I guess.[CSVLB]Senses fail, Saosin, and Avenged Sevenfold have been cranking on my ipod. In the car. rocking 2pac makaveli.[CSVLB]

3out of 5holywaters–First serving of Thyrotabs at 0615 this morning[CSVLB]Good luck. I used that stack last year and looking back on it, it was one of the best I have taken so far when comparing other stacks I have since taken.

5out of 5dema14–anytime bro :

4out of 5boroboro55–Also something on the side delts. you can bend about 45 dgree and perform side laterals. but hold your DBs will your thumbs downward/Elbow high. this movement get your rear portion of side delts working.

5out of 5Some–Current Stats Goal by end of summer

5out of 5gazQ–3caps. Twice a day. With Food. (6caps total)

5out of 5mihalich3–Yup. caffeine 'withdrawals suck. :p[CSVLB]Good to see you're not feeling sleepy. I remember feeling a bit tired when I got off of it for a few days but now I feel just as good without it. You are for sure looking huge in that pic after workout, maybe even a bit leaner but that may be the lighting. Good work either way and keep it up bro![CSVLB]Yup. caffeine 'withdrawals suck. :p

4out of 5MusicInsideYou–Well, off to eat Meal #3. . .[CSVLB]Well, tomorrow doesn't get to be cheat day! Shoot! I'm suffering through one more day because I plan to make Chili Mexican Cornbread for the SuperBowl party I'm having. Oh, well. I still haven't planned out my food for tomorrow. I guess I'll just wing it. Here it is! :)

3out of 5semenof123–Surprised cals were actually that high, so maybe I need to aim for 3500. Carbs will increase since I'm adding more gainer.

5out of 5Horzz–ACTIVE INGREDIENTS Proprietary Blend 5,510mg

3out of 5rbsk20–Pumps:8/10 Decent pumps but nothing extreme