Completed thru 11,800:

[code]
2254^11721-11721^2254
6619^11730-11730^6619
9955^11742-11742^9955
2164^11751-11751^2164
7397^11772-11772^7397
11702^11773-11773^11702
6780^11773-11773^6780
5624^11777-11777^5624
9049^11778-11778^9049 [/code]

The [URL="http://primfakt.atw.hu/"]y^x-x^y PRPs page[/URL] is updated, the new PRPs are on the page now.

[QUOTE]
then sieved and ran 10<=y<="16" for x<=200000 (still running;
[/QUOTE]

Serge, the search to x=200,000 is still running?
What is with the number x<=200,000, 2<=y<=9, you search also
this number?

10<=y<=17 for x<=200000 is done.
[QUOTE=NorbSchneider;434785]What is with the number x<=200,000, 2<=y<=9, you search also this number?[/QUOTE]
No, I have not looked at x<=200,000, 2<=y<=9 because it appears to be finished by others: Donovan Johnson, Henri Lifchitz, maybe some others.

Completed thru 11,900:

[code]
3002^11819-11819^3002
1379^11822-11822^1379
2150^11823-11823^2150
3137^11826-11826^3137
3017^11838-11838^3017
3373^11850-11850^3373
11195^11852-11852^11195
11161^11858-11858^11161
3617^11862-11862^3617
32^11879-11879^32
5520^11879-11879^5520
5046^11887-11887^5046
463^11888-11888^463
[/code]

Completed thru 12,000

[code]
10755^11902-11902^10755
11141^11910-11910^11141
11391^11920-11920^11391
9578^11927-11927^9578
10442^11933-11933^10442
5639^11954-11954^5639
4220^11963-11963^4220
2582^11971-11971^2582
5715^11974-11974^5715
704^11977-11977^704
1578^11983-11983^1578
[/code]

Completed thru 12,100:

[code] 3723^12010-12010^3723
8678^12011-12011^8678
9021^12022-12022^9021
4231^12032-12032^4231
6262^12033-12033^6262
2984^12057-12057^2984
11687^12066-12066^11687
9741^12068-12068^9741
9090^12071-12071^9090
458^12085-12085^458
6659^12092-12092^6659[/code]

Completed thru 12,200:

[code] 2622^12101-12101^2622
2^12103-12103^2
5870^12127-12127^5870
5889^12128-12128^5889
455^12132-12132^455
4820^12141-12141^4820
2106^12143-12143^2106
5922^12155-12155^5922
1175^12162-12162^1175
2495^12168-12168^2495
6867^12170-12170^6867
11163^12172-12172^11163
10626^12175-12175^10626
8132^12183-12183^8132
7590^12193-12193^7590 [/code]

I found the following new PRPs from x=10990, to x=11055

[CODE]
10568^10993-10993^10568
10502^11005-11005^10502
3552^11009-11009^3552
7178^11011-11011^7178
7471^11028-11028^7471
8918^11049-11049^8918
7704^11051-11051^7704
8684^11055-11055^8684
[/CODE]

The [URL="http://primfakt.atw.hu/"]y^x-x^y PRPs page[/URL] is updated, the new PRPs are on the page now.

My reserved range is finally complete. Here are the final primes:

[code] 368^12203-12203^368
10982^12203-12203^10982
271^12210-12210^271
4272^12211-12211^4272
2048^12225-12225^2048
1164^12229-12229^1164
10377^12230-12230^10377
5562^12269-12269^5562
5768^12269-12269^5768
2618^12275-12275^2618
3419^12308-12308^3419
6934^12309-12309^6934
12209^12330-12330^12209
3498^12337-12337^3498
8202^12341-12341^8202
2768^12355-12355^2768
5800^12369-12369^5800
602^12371-12371^602
1962^12373-12373^1962
11971^12374-12374^11971
695^12386-12386^695
9746^12387-12387^9746
145^12392-12392^145
[/code]

I found the following new PRPs from x=11056, to x=11150

[CODE]
9384^11059-11059^9384
1584^11083-11083^1584
774^11089-11089^774
1470^11089-11089^1470
5245^11094-11094^5245
5175^11096-11096^5175
9407^11102-11102^9407
4243^11126-11126^4243
10600^11127-11127^10600
3099^11132-11132^3099
7448^11147-11147^7448
[/CODE]

The [URL="http://primfakt.atw.hu/"]y^x-x^y PRPs page[/URL] is updated, the new PRPs are on the page now.

[QUOTE]
My reserved range is finally complete.
[/QUOTE]

Thank you Mark for searching the x=11301-12400 range, you have found 118 new PRPs.
(One PRP was already known: 2^12103-12103^2)

I found the following new PRPs from x=11151, to x=11300

[CODE]
9253^11168-11168^9253
7493^11178-11178^7493
10413^11182-11182^10413
9560^11187-11187^9560
1364^11201-11201^1364
1784^11221-11221^1784
7742^11229-11229^7742
8101^11232-11232^8101
3479^11240-11240^3479
4448^11243-11243^4448
2606^11267-11267^2606
462^11269-11269^462
11172^11275-11275^11172
563^11280-11280^563
5059^11282-11282^5059
491^11294-11294^491
[/CODE]

From x=12501, to x=12650
[CODE]
6750^12509-12509^6750
9001^12528-12528^9001
7337^12542-12542^7337
8323^12542-12542^8323
11966^12553-12553^11966
6576^12565-12565^6576
6411^12568-12568^6411
2210^12579-12579^2210
3050^12579-12579^3050
4209^12580-12580^4209
4273^12584-12584^4273
5001^12590-12590^5001
9932^12595-12595^9932
5762^12603-12603^5762
6900^12607-12607^6900
9722^12611-12611^9722
1945^12612-12612^1945
228^12631-12631^228
1158^12631-12631^1158
9224^12633-12633^9224
10736^12645-12645^10736
5779^12648-12648^5779
[/CODE]

Other PRPs
[CODE]
97^13088-13088^97
314^13049-13049^314
461^13400-13400^461
588^13231-13231^588
8^60681-60681^8
[/CODE]

I found 2 PRPs on prptop, discovered by Serge Batalov.
42^18385-18385^42
41^23690-23690^41
Serge have you found any other new y^x-x^y PRPs?

The [URL="http://primfakt.atw.hu/"]y^x-x^y PRPs page[/URL] is updated, the new PRPs are on the page now.