Sexy 11

Sexy 11
From Wikipedia, the free encyclopedia

^ D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences . 1 (12). arXiv : 1407.4897 . doi : 10.1186/s40687-014-0012-7 . MR 3373710 .

^ Batalov, S. "Let's find some large sexy prime pair[s]" . mersenneforum.org . Retrieved 3 October 2019 .

^ Kaiser, Peter (May 2019). "sexy prime triplet" . Mersenne forum . Retrieved 13 May 2019 .

^ Andersen, Jens Kruse. "The largest known CPAP's" . primerecords.dk . Retrieved 19 August 2019 .

^ Davis, Ken. "Brillhart-Lehmer-Selfridge provable triplet Oct 2019" . primenumbers yahoo group . Retrieved 2 October 2019 .

^ Andersen, Jens Kruse. "The largest known CPAP's" . primerecords.dk . Retrieved 13 October 2019 .

^ Batalov, Serge. "Consecutive primes arithmetic progression (d=6), Apr 2022" . Primes.utm.edu .

^ Andersen, Jens K. (November 2005). "Gigantic sexy and cousin primes" . primenumbers yahoo group . Retrieved 27 January 2009 .

^ Davis, Ken (September 2010). "1004 sexy prime quadruplet" . primenumbers yahoo group . Retrieved 2 September 2010 .

^ Hubal, Marek (May 2019). "CPAP's sexy prime" . primenumbers yahoo group . Retrieved 10 May 2019 .

^ Andersen, Jens Kruse (May 2019). "Re: CPAP's sexy prime" . primenumbers yahoo group . Retrieved 19 September 2019 .

^ Kaiser, Peter (June 2019). "Let's find some large sexy prime pair (and, perhaps, a triplet)" . Mersenne forum . Retrieved 18 August 2019 .

^ Lamprecht, Gerd; Luhn, Norman (October 2019). "CPAP's sexy prime" . primenumbers yahoo group . Retrieved 13 October 2019 .

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Sexy primes are prime numbers that differ from each other by 6. For example, the numbers 5 and 11 are both sexy primes, because both are prime and 11 − 5 = 6 .

The term "sexy prime" is a pun stemming from the Latin word for six: sex .

If p + 2 or p + 4 (where p is the lower prime) is also prime, then the sexy prime is part of a prime triplet . In August 2014 the Polymath group, seeking the proof of the twin prime conjecture , showed that if the generalized Elliott–Halberstam conjecture is proven, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 6 and as such they are either twin , cousin or sexy primes. [1]

As used in this article, n # stands for the product 2 · 3 · 5 · 7 · … of all the primes ≤ n .

The sexy primes (sequences OEIS : A023201 and OEIS : A046117 in OEIS ) below 500 are:

As of April 2022 [update] , the largest-known pair of sexy primes was found by S. Batalov and has 51,934 digits. The primes are:

Sexy primes can be extended to larger constellations. Triplets of primes ( p , p +6, p +12) such that p +18 is composite are called sexy prime triplets . Those below 1,000 are ( OEIS : A046118 , OEIS : A046119 , OEIS : A046120 ):

In May 2019, Peter Kaiser set a record for the largest-known sexy prime triplet with 6,031 digits:

Gerd Lamprecht improved the record to 6,116 digits in August 2019:

Ken Davis further improved the record with a 6,180 digit Brillhart-Lehmer-Selfridge provable triplet in October 2019:

Norman Luhn & Gerd Lamprecht improved the record to 6,701 digits in October 2019:

Serge Batalov improved the record to 15,004 digits in April 2022:

Sexy prime quadruplets ( p , p +6, p +12, p +18) can only begin with primes ending in a 1 in their decimal representation (except for the quadruplet with p = 5). The sexy prime quadruplets below 1000 are ( OEIS : A023271 , OEIS : A046122 , OEIS : A046123 , OEIS : A046124 ):

In November 2005 the largest-known sexy prime quadruplet, found by Jens Kruse Andersen had 1,002 digits:

In September 2010 Ken Davis announced a 1,004 digit quadruplet with p = 2 3333 + 1582534968299. [9]

In May 2019 Marek Hubal announced a 1,138 digit quadruplet with p = 1567237911 × 2677# + 3301. [10] [11]

In June 2019 Peter Kaiser announced a 1,534 digit quadruplet with p = 19299420002127 × 2 5050 + 17233. [12]

In October 2019 Gerd Lamprecht and Norman Luhn announced a 3,025 digit quadruplet with p = 121152729080 × 7019#/1729 + 1. [13]

In an arithmetic progression of five terms with common difference 6, one of the terms must be divisible by 5, because 5 and 6 are relatively prime . Thus, the only sexy prime quintuplet is (5,11,17,23,29); no longer sequence of sexy primes is possible.

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Try these moves when she’s in the mood for something a little more intense
In the emotional sense, staring into each other’s eyes and synchronizing your breath for deep, passionate sex can be mind-blowing . But what if you’re looking to literally go deep?
As long as your partner is on board, that can be hot, too.
Here are the 11 most penetrating sex positions for when you’re both in the mood for something intense.
How to Do It
She lies facedown with her hips slightly elevated (try sticking a pillow underneath them) and her legs straight, spread out slightly.
Why It Works
The lifted hips offer a low barrier to entry, says New York City sex therapist , Ian Kerner, Ph.D., author of She Comes First .
Perks
This one gives her great G-spot stimulation, says Kerner.
How to Do It
While you sit down, she sits in your lap, facing you.
Why It Works
Because her legs are spread wider here, she’s more open to receiving all you have to offer, Kerner says.
Perks
From here, she’s able to control the pace and just how deep she wants you to go.
How to Do It
Like cowgirl, she’s on top pushing off of you as you lie back. The twist here is that you assist with your hands. By holding her hips or thighs, you’ll support her weight and rise to meet her thrusts.
Why It Works
This gives her some great G-spot stimulation, and she can go as deep as she likes depending on her thrusts, says Kerner.
Perks
Great view, and she get the chance to dominate, he says.
How to Do It
She’s on top as you lie back. She pushes off of your chest and slides against your thighs.
Why It Works
From here, says Kerner, she can open her legs wider for a deeper entrance.
Perks
This move gives G-spot and clitoral stimulation, which means she’s twice as likely to get off, he says.
How to Do It
Lay on top of her, face to face, as she lies on her back.
Why It Works
It’s a classic for a reason—this one gives you both deep stimulation, combined with intimacy , Kerner says.
Perks
There’s lots of eye contact and face time for making out , says Kerner.
How to Do It
Kneel directly behind her as she’s on her hands and knees.
Why It Works
The angle of this position gives deep penetration and G-spot stimulation, says Kerner.
Perks
Your hands are free to stimulate her clitoris or engage in a little nipple action, he says.
How to Do It
You’re seated. She backs into your lap, facing away from you.
Why It Works
Since this probably isn’t your go-to position, it’ll feel like a whole new world, says Kerner. That newness will make the penetration feel deeper than it actually is.
How to Do It
Lie side-by-side in the spooning position, and enter her from behind.
Why It Works
You have more leverage and support so you can wedge yourself in a way that creates maximum depth, says Kerner.
Perks
There’s plenty of G-spot stimulation for her this position, he says. Plus, it’s perfect for when you’re both tired but still in the mood.
How to Do It
Lie on your back with legs raised up and out. Get your ankles as far back toward your head as you can. Then, he enters in a missionary position .
Why It Works
The legs are spread wide, lending more depth, says Kerner.
Perks
He’s riding high, so that will give you some clitoral stimulation—or you’re free from here to take that into your own hands , he says.
How to Do It
She lies back in the plow position , ankles on either side of her head. You squat and dip your penis in and out of her.
Why It Works
This one is all about the newness , says Kerner. In this strange, new position, every sensation feels amplified.
Perks
All the blood will start rushing to her head, adding to the fresh sensations, he says.
How to Do It
He sits cross-legged, then you sit on his lap, facing him. Next, wrap your legs around his back, pull each other closer, and rock back and forth .
Why It Works
This position is all about opening yourself up—especially your legs and hips, he says.
Perks
Here, you can get deep in more ways than one: Lock eyes with your partner as you climax for added intimacy, says Kerner.
The article 11 Must-Try Positions for Super-Deep Sex originally ran on WomensHealthMag.com.
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