Problem Ten revisited

[gd_barnes]

5200 thru 5299 is complete. It went to the multiply side for 5256 & 5272.

Primes:

p(5200)#/p(910)+1
p(5201)#/p(12)-1
p(5202)#/p(169)-1
p(5203)#/p(1044)-1
p(5204)#/p(1403)+1
p(5205)#/p(765)-1
p(5206)#/p(1411)-1
p(5207)#/p(49)+1
p(5208)#/p(1535)+1
p(5209)#/p(449)-1
p(5210)#/p(1257)+1
p(5211)#/p(997)+1
p(5212)#/p(2184)-1
p(5213)#/p(972)-1
p(5214)#/p(577)-1
p(5215)#/p(976)-1
p(5216)#/p(2697)-1
p(5217)#/p(665)+1
p(5218)#/p(934)-1
p(5219)#/p(378)-1
p(5220)#/p(256)+1
p(5221)#/p(3145)-1
p(5222)#/p(388)-1
p(5223)#/p(1567)-1
p(5224)#/p(815)-1
p(5225)#/p(3707)-1
p(5226)#/p(3434)-1
p(5227)#/p(524)+1
p(5228)#/p(1443)+1
p(5229)#/p(1139)-1
p(5230)#/p(360)-1
p(5231)#/p(4343)+1
p(5232)#/p(2330)-1
p(5233)#/p(435)+1
p(5234)#/p(1810)+1
p(5235)#/p(126)+1
p(5236)#/p(173)-1
p(5237)#/p(14)+1
p(5238)#/p(258)-1
p(5239)#/p(2854)+1
p(5240)#/p(403)+1
p(5241)#/p(241)-1
p(5242)#/p(2115)-1
p(5243)#/p(524)-1
p(5244)#/p(2729)+1
p(5245)#/p(2439)-1
p(5246)#/p(1739)-1
p(5247)#/p(2568)+1
p(5248)#/p(39)+1
p(5249)#/p(1346)+1
p(5250)#/p(2272)-1
p(5251)#/p(50)-1
p(5252)#/p(795)+1
p(5253)#/p(991)+1
p(5254)#/p(664)-1
p(5255)#/p(1778)+1
p(5256)#*p(626)+1
p(5257)#/p(2264)+1
p(5258)#/p(160)-1
p(5259)#/p(67)-1
p(5260)#/p(2184)+1
p(5261)#/p(1205)-1
p(5262)#/p(2697)+1
p(5263)#/p(1021)-1
p(5264)#/p(941)-1
p(5265)#/p(2723)+1
p(5266)#/p(1774)-1
p(5267)#/p(223)+1
p(5268)#/p(658)-1
p(5269)#/p(2535)+1
p(5270)#/p(347)+1
p(5271)#/p(208)+1
p(5272)#*p(1907)+1
p(5273)#/p(321)-1
p(5274)#/p(488)-1
p(5275)#/p(87)-1
p(5276)#/p(335)+1
p(5277)#/p(256)+1
p(5278)#/p(1180)+1
p(5279)#/p(1696)+1
p(5280)#/p(475)-1
p(5281)#/p(1857)+1
p(5282)#/p(53)+1
p(5283)#/p(1895)+1
p(5284)#/p(2812)-1
p(5285)#/p(2220)-1
p(5286)#/p(1232)-1
p(5287)#/p(2191)+1
p(5288)#/p(1001)+1
p(5289)#/p(47)+1
p(5290)#/p(2489)-1
p(5291)#/p(531)-1
p(5292)#/p(837)+1
p(5293)#/p(1267)+1
p(5294)#/p(835)-1
p(5295)#/p(44)+1
p(5296)#/p(1523)+1
p(5297)#/p(1297)+1
p(5298)#/p(442)+1
p(5299)#/p(2728)-1

All primes are proven.

[Harvey563]

5100 thru 5199 complete, reserving 5300 thru 5399

went to * for 5114, 5150, 5192, 5195

[Harvey563]

5300 thru 5399 complete, reserving 5400 thru 5499

went to * for 5347 & 5364.

[Harvey563]

Hi,

I am writing to report that a counterexample has been found to the conjecture in Puzzle ten of the Prime Puzzles and Problems Connection,
http://www.primepuzzles.net/puzzle/puzz_010.htm
http://www.primepuzzles.net/puzzle/puzz_010.htm

The prime 53819, the 5843rd prime, is composite for all values of the equations:
p(5483)#/p(k)-1
p(5483)#/p(k)+1
p(5483)#*p(k)-1
p(5483)#*p(k)+1. where k is < or = 5483.
5483 is the smallest such value.

Mark Rodenkirch contributed cycles, custom sieves, and pfgw scripts, and deserves much of the credit. Other contributors include Anderson/Robinson(p21), Gary Barnes,Peter Benson(p67), D. Heuer(p16), T. Rajala, H. Rosenthal(p10); T. Sorbara, and Stephano D'Urso.

Details at http://harvey563.tripod.com/puzzle10.html
http://harvey563.tripod.com/puzzle10.html

Steven Harvey

[rogue]

Don't forget Robert Gerbicz with his sieving idea. That reduced the PRPing time significantly.

Note that in post 74 of this thread that you suggested sieving from p(5000) to p(6000) (instead of p(10000)). Although that never happened, the solution was found before p(6000).

[Harvey563]

I did just sieve to 6000, and I lucked out.

Thanks to RG for the sieving idea!

Steven

[Merfighters]

Originally Posted by Harvey563

http://www.primepuzzles.net/puzzle/puzz_010.htm

The correct link is: http://www.primepuzzles.net/puzzles/puzz_010.htm

[gd_barnes]

Congrats Steven! The testing was growing increasingly lengthy so it's nice to see the conjecture finally disproven.

[Harvey563]

here's part one.

[Harvey563]

& here's part 2.