la solitudine dei numeri primi "Prime numbers are divisible only by 1 and by themselves. They stand in their place in the infinite series of natural numbers, squashed in between two others, like all other numbers, but a step further on than the rest. They are suspicious and solitary, which is why Mattia thought they were wonderful. Sometimes he thought that they had ended up in that sequence by mistake, they they'd been trapped like pearls strung on a necklace. At other times he suspected that they too would rather have been like all the others, just ordinary numbers,but for somereason they weren't capable of it. In his first year at university, Mattia had learned that, among prime numbers, there are some that are even more special. Mathematicians call them twin primes: they are pairs of prime numbers that are close to one another, almost neighbours, but between them there is always an even number that prevents them from truly touching. Numbers like 11 and 13, like 17 and 19, 41 and 43. lf you have the patience to go on counting, you discover that these pairs gradually become rarer. You encounter increasingly isolated primes, lost in that silent, measured space made only of numbers, and you become aware of the distressing sense that the pairs encountered up until that point were accidental, that solitude is the true destiny. Then, just when you're about to surrender, when you no longer have any desire to go on counting, you come across another pair of twins, clutching each other tightly. Among mathematicians there is a common conviction that however far you go, there will always be another two, even if no one can say where exactly, until they arediscovered".
www.mathrecreation.com - @ Dan MacKinnon - 2012 i bought this book several years ago, initially attracted just by its cover (like it often happens to me). then this story about numbers has really caught me up. since then the book has become famous, translated in many languages and made into a movie, while the pattern it inspired me languished until now. i hope you'll appreciate this belated effort and its understated result: a (literally!) infinite cowl in a classic and simple stitch, yet revised and corrected with neat details - actually playing by numbers... insights the book Paolo Giordano, The solitude of prime numbers, 2008 primesoverview http://en.wikipedia.org/wiki/Primenumbers http://en.wikipedia.org/wiki/Twin_prime tables http://oeis.org/A000040 http://arnflo.se/\~site_ files/Other/twinprimes http://korn19.ch/coding/primes/twins.php video http://www.youtube.com/watch?feature=player embedded&v=7wFjieSzQdU a wonderful representation from this excellent site: www.sievesofchaos.com
needles: 4 mm/US 6 - 4.5 mm/US 7
materials
skill level: intermediate gauge not important
Size you choose! - in this project: 10cm width - 380cm circumference yarn: a soft DK - used here, in shade Tern: madelinetosh tosh dk - 100% merino - one skein = 206m/225 yds - 2 full skeins used. the same yardage with thinner yarn and smaller needles could be an interesting alternative for a lighter result. notions: yarn needle knitting references crochet cast-on: http://newstitchaday.com/how-to-knit-the-crochet-provisional-cast-on/ brioche stitch: a highly due tribute to the master of this timeless stitch, Nancy Marchant, whose site and book are a must for any knitter and a goldmine of information. for a condensed tutorial see also here.
directions
the diagram above shows the start sequence of primes (A) spaced by one of the two occurring detachments - primes gap (B) or twins separation (C). in the table below you got a list of primes showing the first 36 twins (separated by the red line) - the smaller numbers above them are the gap between primes (just for knitting convenience).
| 1 | 4 | 4 | 4 | 6 | 9 4 | 4 | 6 | 6 | 6 | |||||||||
| 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | |
| 4 | 6 | 4 | 6 | 8 | 4 | 4 | 4 | 14 | 4 | 9 | 10 | |||||||
| 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | |
instructions
provisionally crochet C0 an uneven number of sts (in this case 23 sts: 2 edge sts - 19 sts pattern - 2 edge sts). following the provided tables or charts - and the directions about needle sizes - work the two set up rows and then start the sequence: 2xA - B [just row 1and row 4] - 3xA - C - 5xA - C -7xA - B [rows 1-4] -11xA - C - 13xA -. - 23xA - B [row 1 - rows (2-3)×2 - row 4] - 29xA -. - 89xA - B [row 1 - rows (2-3)x3 - row 4] -..- 113xA - B [row 1 - rows (2-3)x6 - row 4] - my two skeins allowed me to get to number 59, but you can proceed indefinitely, of course! number you've completed, work the following suitable gap/separation to row 3. onal CO and the set up rows and graft together the two ends of the cowl or make a 3 needle bind off to join then
@ceciknits 2013 - ceciknits@gmail.com tables
| set up rows (smaller needles) | repeatrows1-2foreveryprimeunit (i.e.: 3 times for 3, 11 times for 11, etc.) except for the gap between primes 2 and 3 (which is just 1), in the initial | |
| 1 | (RS): slp1wf, k to last st, slp1wf | |
| (brioche set-up row): (k1, slp1wf), *k1, yos; rep from * to last 3 sts, k1, ( slp1wf, k1) | ||
| A brioche (bigger needles) 1 | ( ) ( ) :()) | |
| (k1, slp1wf), Ibrk, *yos, brk; rep from * to last 2 sts, (slp1wf, k1) | ||
| B | primes gap / stst (smaller needles) | range of primes this gap consists mostly of 4 units (rows 1-4). for bigger gaps - 6 or more units - repeat rows 2-3 one or more times. |
| 1 | (RS) (brioche end row): (slp1wf, k1), *k1, brk; repeat to last 3 sts, k1, (k1, slp1wf) (k1, slp1wf), p to last 2 sts, (slp1wf, k1) | |
| ２ | slp1wf, k to last st, slp1wf | |
| 3 4 | brioche set-up row | |
| C | twins separation / eyelets (smaller needles) | |
| 1 | (RS) (brioche end row): (slp1wf, k1), *k1, brk; repeat to last 3 sts, k1, (k1, slp1wf) | |
| k1, p2tog to last 2 sts, (slp1wf, k1) | ||
| 3 | (slp1wf, k1), *yo, k1; repeat to last st, slp1wf | |
| 4 | ||
| brioche set-up row |
charts
abbreviations: provisional CO k: knit p: purl Oyo: yarn over slp1wf: slip one stitch purlwise with yarn in front △p2tog: purl two stitches together mbrk (brioche knit): knit the stitch that was slipped in the previous row together with its yarnover yos (yo, slp1wf): bring the working yarn to the front of the work, slip the next stitch purlwise, bring the yarn over the right needle to the back of the work, ready to work the next stitch mIbrk (lifted brioche knit): lift the horizontal thread of the previous fyos on left needle from front to back, and knit it together with the stitch that was slipped in the previous row edge sts pattern repeat finishing: weave in ends. wash, squeeze gently to remove the excess of water and let dry almost completely on a flat surface. to even the edges and stretch the fabric lenghtwise, while stilla bit damp hang the cowl with a light weight into the loop (a small water bottle wrapped up in a towel works well) taking care to displace the hanging point and the weight from time to time to avoid excessive tension in the fabric. wear as you prefer but always with infinite joy!
@ceciknits 2013 - ceciknits@gmail.com
