Problems & Puzzles: Puzzles

 

 

Problems & Puzzles: Puzzles

Puzzle 1246 A follow-up to Puzzle 1242

Shyam Sunder Gupta sent a follow-up to Puzzle 1242, ands wrote on Oct 27, 2025:

I have investigated the puzzle for cube and reverse also, and the smallest examples of "3, 4 & 5 primes" are given below:

a) p1 = 5 -> p2 = 521 -> p3 = 167024141.

b) p1 = 41243 -> p2 = 70957362735107 ->
p3 = 340072580562292758983063684559587385662753 ->
p4 = 7771387902509461541804448596476171134994618019090021926170209536132534500779209350826609131671267667238
6860916228621367192393.

c) p1 = 11217940001 -> p2 = 1000283544657170636980000961141 ->
p3 = 1226272077252711947390945706425645203529615506075666763701999365951325413406207815780580001 ->
p4 = 100047145658058318593979730778331416039914635950352433760665777316716445290784151466967668560587748
58791100911195180044557430738541444309411451294908378744129380397940195260370815724270212201975137786307
12147757747734834125822621875520756184650146211676326793566038993481 ->
p5 = 1463076912982113627169683307080233968332127412643952920249551233336733
1928669243078600367519260936882087066057019084414786667360450552531102
6081347929012558226140017088148937551854618601902651614078540153622170
6213657192423941122453492805695549493243620499604092396589818815221817
7814890671161471144188095822226502922208208905055663189003969729095745
5612603465881188740134621847102430336606238321144136009146389850335826
7546255986917267500754051361228583361414916791605644052837437603579803
5268679980869767413162546732983830799588112788151085444905524028392571
5169422118668970115545627398078512018026643746076332660725094433713248
6488471224604338146738998046511392083753555523673776157338892124890668
9330258719799373856933517345329609746706346745930366613853277344889173
30603904919080346456293592640666305141001.   

Q. Send your largest sequence of primes for this procedure.  

From 16-21 Nov. 2025, contributions came from Paul Cleary

***

Paul wrote:

I couldn't find any more than 5 primes in sequence, here are the ones I found.
start prime 33372696859 (11 digits)  chain length 5,
start prime 193092141559 (12 digits)  chain length 5,
start prime 208127656829 (" ")  chain length 5,
start prime 219946382059 (" ")  chain length 5,
start prime 235298926517 (" ")  chain length 5,
start prime 245570947003 (" ")  chain length 5,
start prime 259151351729 (" ")  chain length 5,
start prime 265607153741 (" ")  chain length 5,

For this last one the complete sequence is:

StartPrime -> 265607153741,
 
 12084034150634038304575530403873781,
 
 14583206005183657896395134906354910530263481569409220913737117706588
19877565430205630439116809657554671

11735612549742202037219274476651323125917985297178213432843875150473
3060681230093290228158615729421542135076107175044352560654655737775480
9927397621946912146321130350027423876417811095707897401755065058854184
7357488975744547449499619442618565682289862786767351086649967021770776
60677428243827614374298041013,
 
 79198756695713756540011582381531013168120169006940251063170908704435
6700434063189882405142490093169957414858088838455240673298189188335298
1982603747963237597862756006034241927140219186750580214995176891655475
2856738461776290166620184360776742850131282798131084125970160193298147
2523197404274195607013385107733863364435902283291328549371593670535689
8080583599737900522960146379418556664470347426188459377213442479798343
9596096095099936346622982841510967954516172979950849654743219261418748
7385718575359014670780142807040344923889852886860212794709321306446215
4850435359246282876710995204895796091430675433281687909943867377589357
2859439809344318779643675735532480771530563687759356184986365461918873
5808444232484876077538416358468316512048127195762874171016458686159239
2947467922690716712477812850273462247035793018642774364222454074895420
1738016426730256583969246160654498352437889840053835432933839599871237
66652826161

There were many hundreds of chain length 4.  I went up to prime 297961870543 before stopping

***

 

Records   |  Conjectures  |  Problems  |  Puzzles