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prime

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.
However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
The property of being prime is called primality. A simple but slow method of checking the primality of a given number



n


{\displaystyle n}
, called trial division, tests whether



n


{\displaystyle n}
is a multiple of any integer between 2 and





n




{\displaystyle {\sqrt {n}}}
. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018 the largest known prime number is a Mersenne prime with 24,862,048 decimal digits.There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled. The first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen large number being prime is inversely proportional to its number of digits, that is, to its logarithm.
Several historical questions regarding prime numbers are still unsolved. These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers. Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals.

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  1. nick9one1

    prime t&g redwood before hardiebacker?

    I'm making progress with my ensuite wetroom, and I'm nearly at the point of tiling. The form is 7-8mm above the floor, so I plan to bring up the level with 6mm hardiebacker. I've read conflicting information on weather the t&g should be primed before I use tile adhesive to stick down the...
  2. G

    Do I prime skimmed and bare plastered board walls before tiling?

    I have recently stripped the bathroom. I have 2 walls in non water area. One wall is new plasterboard and the other wall is skimmed plasterboard that I have managed to get most of the paint off though planing to use a 120grit orbiter to clean off any loose pain Both these walls will be tiled...
  3. lukeoflondon

    How do I prime floorboards before aquapanel?

    Hi everyone, sorry if this is an incredibly stupid thing to ask: I have some old 18mm floorboards, on top of which I plan to lay aquapanel. I was going to use some kind of cement-based flexible adhesive between the floorboards and the panel (haven't decided exactly what yet), and I'm sure I need...
  4. B

    To prime or not to prime?

    Hello there... first post and all. I've just had a kitchen extension finished by the builders and there's all sorts they gave me advice on but they argued amongst themselves on the primer. The screed is set and has been for 2 months and I'm about to self level it with latex compound since...
  5. R

    My 1st Job prime or tank first?

    This is a proper newbie question. I've tried to find the answer already provided on the forum but can't! Is the order of application that you prime, tank, tile or tank, prime, tile? Or just two things? - prime and tile or tank and tile? I specifically have a wall that is pink plastered...
  6. G

    Do I need to prime

    I am tiling our kitchen splashbacks with metro ceramic tiles. The old brick /plastered walls were originally painted which I have sanded scraped and scored ....do I need to prime the walls and if yes what product goes best with Weber set plus white adhesive . Any comments appreciated and...
  7. R

    Porcelain Do I need to prime my existing floor tiles?

    Hello I currently have porcelain tiles on the floor, and I want to put new porcelain tiles ON TOP of them (they'll be 90x90cm). Do I have to prime the existing tiles? Or will cleaning them be enough? Thank you
  8. TTID

    My 1st Job Prime Hardiebacker for tanking

    Hi long time reader first time posting. I know hardiebacker does not need to be primed normally but when tanking a shower areas with the Mapei kit do I prime the boards or not? Thanks
  9. R

    How to prime sand and cement rendered walls with the top coat of gypsum plaster removed?

    Afternoon everyone, just after a bit of advice on preparing some walls for ceramic, possibly porcelain (haven’t decided yet) wall tiles. Okay so a bit of background information first of all, the gypsum finish plaster on all the walls in my new house is quite poorly adhered in most places, it...
  10. Tom TGH Tiling

    Bathroom wall prep

    Hi guys, I'm currently re-tiling my own bathroom. My plan after ripping off the old tiles was to prime with sbr, level with rapid set adhesive, then start tiling. Looking at the wall I'm thinking I should take off all the plaster, then mechanically fix marmox boards onto a bed of adhesive...
  11. N

    Prime old plastered walls

    Evening all, Quick question on priming old walls. Original plaster is in reasonable condition, some minor imperfections etc. Do i need to prime the walls before tilling old plaster? Thanks!
  12. S

    BAL BAL Prime APD on Cement Board - Dilute or Not?

    I’m about to tank Hardie Backer cement boards using the BAL WP1 waterproofing kit. I’m a bit confused with the Prime APD. Should I just paint this straight on, undiluted, or should I be diluting at all? If I do need to dilute, what proportions? Cheers.
  13. S

    Prime Plasterboard before tiling

    Hi All, I decided to strip all of the old plasterboard off the walls in my bathroom (as opposed to overboarding) and will be installing new plasterboard. I will be tanking the shower enclosure with the Bal WP1 kit. I will be fitting 600mm x 300mm porcelain tiles. Do I need to prime the...
  14. B

    Preparation Tiling to plasterboard - to prime or not to prime?

    Hello, Tried to read previous posts but all seem to say different things or depend on adhesive. Bathroom has been plasterboarded, I will be using Aquaseal Wet Room System to tank the shower area and around the bath. I plan on using Mapei cement based wall & floor tile adhesive, the tiles I...
  15. C

    Tiling onto tiles should I prime?

    Hi all. There is a job coming which requires tiling directly onto an allready tiled wall. The existing tiles are of sound condition no breaks or loose etc, in fact there solid on. They are onto concrete. They are glazed but I was going to score and take the glaze off best as possible...
  16. C

    why prime the back of the ply and not the front?

    Hey folks, ive just laid 12mm Marine ply on my bathroom floor in preparation for tilling, its screwed down on 200mm grid formation then i primed the ply with SBR bond as i have done in the past. Today i mixed up sovereign tile adhesive and glanced at the instructions which stated i was to prime...
  17. D

    Basic advice needed

    Hi, I have read several threads, but am still unsure of what to do with my bathroom. I have 400mm x 400mm X 9mm porcelain tiles to use on my bathroom walls. The walls are bare brick, but uneven so I am going to batten them and screw boards onto this. I haven't bought the boards yet, and was...
  18. Andy Allen

    Amazon prime

    Anyone got it? What's it like? How does it work....is it streamed live to your TV. ...do you need a box of some kind ....or can you only watch it on a laptop.
  19. F

    Painted Walls And Prime + Grip

    everytime I walk into a room to tile and I see painted walls, I always worry! A lot of the time I've removed any loose with a scraper and scored the rest a bit with Stanley knife, primed with the usual acrylic and tiled with single part flexi and never had an problems. I've got a job to do next...
  20. R

    Should I have used SBR to prime on top of floor levelling compound

    Hi all, I've been reading all your helpful advice to everyone, so after tearing my hair out for most of the day thought I would sign up. Please could someone clarify if I should've used Cementone SBR on top of a self levelling latex floor compound. I originally stripped the old kitchen floor...
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