Checking whether a certain number is prime

Question

Using the primality test on this site, I found that the concatenation of the digit reversal of the first 548 odd primes in the reverse order is a prime!. It is only a 1998-digit prime, but it took more than an hour for the site's calculator to state that it is a prime.

The calculation went super slowly. Could someone here confirm that this result is correct?.

The result I got is 7693749334931393 ... 91713111753.

Are you asking how to check if a number is prime using Mathematica? If so, try PrimeQ. — bobthechemist, Jan 16 '19 at 02:27
Here's a free (fast) way to test this. It gives True in under a second. It's just building off free Wolfram Cloud stuff so you can give that a check too if you need something else like this. It takes like half a second for the notebook to load, but after that you can do whatever with it. — b3m2a1, Jan 16 '19 at 03:00
Welcome to Mathematica.SE. Are you sure you are posting on the right site? There is nothing in your question making it clear that it is concerned with Mathematica software. — m_goldberg, Jan 16 '19 at 03:33

OkkesDulgerci · Accepted Answer · 2019-01-16T12:55:25.490

You are right!!

    Reverse /@ Table[IntegerDigits[Prime[i]], {i, 549, 2, -1}] // 
   Flatten // FromDigits // PrimeQ

True

7693749334931393929332939193719311937093988318837783368335831583748333\ 8332831283308379733973977396737673167393733373727391739073107379631963\ 7763376317639563346373631363326371633163706339533853185317539553755374\ 5314539353335392537253715311539943194396437643364316437543944333433143\ 7043193398333733173316339533743334331333923332339133313370331033992317\ 2395237523352315239223122371239023302319137813181396137613361373131213\ 9113901398033803970376031603940314037303320391031103100399921792969236\ 9275923592939272927192909230927982788297821682758215823482738233829182\ 3082108279721972987277727672357294721472137292729172317211727072996239\ 6298627862386277621762366295627562746233621262716290623952195297527552\ 1552945234529352135212523052774237427642954274421442734232427142114299\ 3239329832383218327732173275321532743214329332333211329032792239227822\ 1822372296227622152234229322732212223122702230229712161235123412141273\ 1213129212311211129902980278023802180296023602350293029202720271021102\ 3002999179913991789197913791159194913391139131917091109198819781778137\ 8117817681168174811381328111811081987178713871777195713571747114713371\ 3271127190719961796139619661766136617561736172611261916131619061706110\ 6179513851975117517651955135519451345113513251115199413941984178413841\ 1841174195413541154174419341334192417241324190419931183137317631163172\ 3112319131703130311031792119219821382197217721952194217321132192213221\ 7121312110213911781118111711361135111511921132117111901130117901390119\ 0178019601360116011501940193013301130112019101310190017991993897791797\ 6935974914973992991911970978838818877836895875835893892872832812811890\ 8797787377967167757157347937337727917907107196386776376166956356746346\ 1461369167163167061069953957857751759653657557451453251259053059941947\ 8497476436416475494434493433413412491490410479398338397337376395335394\ 3743733133713313113703392382182772172962362752152142932332922722322112\ 9917913911911819713717613617511519419317311317213119017013011017998389\ 73717761695357434147313923291713111753

AAHHHH..., I LOVE YOU MAN !!!!! – Toni S Jan 16 '19 at 02:46 — Toni S, Jan 16 '19 at 02:46
I WILL REMEMBER YOUR NAME !!! : D – Toni S Jan 16 '19 at 02:47 — Toni S, Jan 16 '19 at 02:47

score 2 · Answer 2 · answered Jan 16 '19 at 02:31

2

junk = Table[
   FromDigits@Reverse@IntegerDigits[Prime[i]], {i, 2, 549}];
final = FromDigits[Flatten[IntegerDigits /@ junk]];
PrimeQ[final]

(*

False

*)

This takes $0.002238$ seconds on a Mac laptop.

answered Jan 16 '19 at 02:31

David G. Stork

41,180
3
34
96

Note that it is the first 548 odd primes, 3,5,7,11,13,.... and not the first 548 primes. – Toni S Jan 16 '19 at 02:33
@ToniS: That's why the iteration starts at $i = 2$ (and goes to $549$): Because Prime[2] = 3. And Prime[548] = 3947 and Prime[549] = 3967. – David G. Stork Jan 16 '19 at 02:35
Damn it !! I hate this ! – Toni S Jan 16 '19 at 02:38
Are you sure the first digit of this prime is 769374933493... ? – Toni S Jan 16 '19 at 02:40
1

Nope: $35711317191329213731434\ldots 193919332939293139334937493$. Over and out. Good luck. – David G. Stork Jan 16 '19 at 02:42
@DavidG.Stork - Your Table is running backwards. – Bob Hanlon Jan 16 '19 at 02:51
@BobHanlon: How do you interpret "the concatenation of the digit reversal of the first 548 odd primes"? (Not, the digit reversal of the concatenation of the first 548 primes." – David G. Stork Jan 16 '19 at 03:50
@DavidG.Stork - there are two reversals mentioned: "concatenation of the digit reversal of the first 548 odd primes in the reverse order". The primes in the reverse order requires your table iterator to be {i, 549, 2, -1} – Bob Hanlon Jan 16 '19 at 03:56

Checking whether a certain number is prime

2 Answers2