Below is a gwbasic program that gives prime numbers infinitely. It is of course limited with the capacity of the computer and the programming language's infrastructure.

This program uses an algorithm generating prime numbers as a series, without examining any of them by dividing into any previous primes.

It is not, however, proved in terms of mathematics. We could just test first 1000 primes listed and some random numbers smaller than 500.000, which all came out as prime numbers.

The program can count primes up to 200.000 because there are certain numbers in the series that must be skipped, and the greater the primes become, the more numbers the computer has to store in memory. Those numbers stored are only measures to calculate the numbers to be skipped in the series, so that all the outcoming numbers will be prime.

It gives all the primes, without missing any, and never gives any number that is not prime, as far as we tested. But as I said, it is a matter of mathematical knowledge to proof (or disproof) it, and it is a matter of memory and cpu power to obtain greater primes.

I will be thankful if you comment on the program.

1 dim aday(9000):dim adarti(1200):dim atta(800)

10 var=1:gel=1:winner=1:aday(1)=6:varti=1:garti=1:winnerti=1:adarti(1)=8

11 varta=1:gelta=1:winta=1:atta(1)=9

15 tellioglu(1)=4:tellioglu(2)=20:seferoglu(1)=8:seferoglu(2)=28

17 input "kaca kadarki asallar yazilsin";j

20 a=a+1

40 asal=(6*a)-1:bir=-1

45 if a=aday(winner) then goto 50

47 goto 500

50 if var=gel then var=var+1:aday(var)=(var*7)-1

52 aday(gel)=aday(gel)+(gel*6)-1

54 winner=var

55 for ad=2 to var

70 if aday(var-ad+1)=aday(winner) then aday(var-ad+1)=aday(var-ad+1)+((var-ad+1)

*6)-1

73 if aday(var-ad+1)<aday(winner) then winner=var-ad+1

80 next ad

90 gel=winner

200 asal=(6*a)+1:bir=1

210 if a=adarti(winnerti) then goto 215

212 goto 243

215 if garti=varti then varti=varti+1:adarti(varti)=(varti*7)+1

218 adarti(garti)=adarti(garti)+(garti*6)+1

220 for ad=1 to varti

230 if adarti(varti+1-ad)<adarti(winnerti) then winnerti=varti+1-ad

235 next ad

237 if adarti(garti)-(garti*6)-1=>adarti(winnerti) then adarti(winnerti)=adarti(

winnerti)+(winnerti*6)+1:goto 220

242 garti=winnerti:pasgec=1

243 if a=atta(winta) then pasgec=1:goto 245

244 goto 260

245 if varta=gelta then varta=varta+1:atta(varta)=(varta*5)-1+((varta*6)-1)

246 atta(gelta)=atta(gelta)+(gelta*6)-1

248 for ad=1 to varta

254 if atta(varta-ad+1)<atta(winta) then winta=varta-ad+1

256 next ad

257 if atta(gelta)-(gelta*6)+1=>atta(winta) then atta(winta)=atta(winta)+(winta*

6)-1:goto 248

258 gelta=winta:pasgec=1

260 if a=tellioglu(1) then goto 280

261 if a=seferoglu(1) then goto 290

270 goto 300

280 tellioglu(3)=tellioglu(2)+(tellioglu(2)-tellioglu(1))+12

281 tellioglu(1)=tellioglu(2)

283 tellioglu(2)=tellioglu(3)

284 pasgec=1

285 goto 261

290 seferoglu(3)=seferoglu(2)+(seferoglu(2)-seferoglu(1))+12

291 seferoglu(1)=seferoglu(2)

293 seferoglu(2)=seferoglu(3)

294 pasgec=1

300 if pasgec=1 then pasgec=0:goto 20

500 rem

700 if asal>j then end

710 print asal;

730 if bir=1 then goto 20

740 goto 200

If anyone interested, I can also try to explain the function to generate these series.

Greetings,

Burcin Aydogdu

>There are far shorter algorithms

Cheers

Bob

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