Problems & Puzzles: Puzzles

Puzzle 147.  Twin & reversible primes

The first non trivial example of twin & reversible primes is:

(71, 73) & (17, 37)

A somewhat larger example is:

(173313197, 173313199) & (791313371, 991313371)

One more example I have calculated for this puzzle is:

(10^60+68599471, 10^60+68599473) & (17499586*10^53+1, 37499586*10^53+1)

Question:

Calculate a) a semi-titanic couple b) a titanic couple

Jim Fougeron found (11/1/2002) larger examples of the asked pairs, still not a semi-titanic (500 digits) but large enough to make a record by the moment:

Sub titanic twin/reversible pair of primes:

244909752*809#-1 & 244909752*809#+1 and their reverses.  These are
all 341 digits in length.  They have been proven.  The primorials
using N+1 and N-1 proving techniques, and the reverses by using
ECPP with Primo.

Here are the expanded forms:

244909752*809#-1
928062018516027919593015654952392007884049452133361393716590
124875109935157427807098311906265022073108514282881621049445
449102273154312271007547102727569493270274380318853077771489
952353573686998025706149170380122336228389501475680847773612
187258820238957154928292297037244068743909043939206586014530
51834078065146621961586535712689123624079

244909752*809#+1
928062018516027919593015654952392007884049452133361393716590
124875109935157427807098311906265022073108514282881621049445
449102273154312271007547102727569493270274380318853077771489
952353573686998025706149170380122336228389501475680847773612
187258820238957154928292297037244068743909043939206586014530
51834078065146621961586535712689123624081

Rev(244909752*809#-1)
970426321986217535685169126641560870438150354106856029393409
093478604427307922928294517598320288527812163777480865741059
838226332210830719416075208996863753532599841777703588130834
720723949657272017457001722134513722019445449401261882824158
013702205626091138907087247515399015784210956173931633312549
40488700293259456510395919720615810260829

Rev(244909752*809#+1)
180426321986217535685169126641560870438150354106856029393409
093478604427307922928294517598320288527812163777480865741059
838226332210830719416075208996863753532599841777703588130834
720723949657272017457001722134513722019445449401261882824158
013702205626091138907087247515399015784210956173931633312549
40488700293259456510395919720615810260829

***

J. K. Andersen wrote:

The smallest case with semi-titanic twins is
(10^499+174295123051, 10^499+174295123053) &
(150321592471*10^488+1, 350321592471*10^488+1).
The GMP library made prp tests. Primo proved the primes.

***

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