Hi folks >Humankind to the universe: >> We are d**n sure that (10^86453-1)/9 is prime, >> but we can't d**n well prove it. >> If you know how, we would like to talk to you, please. Love it. This is humanity in a nutshell... we may blow the trumpets of our successes yet we're well aware of our comparatively dismal failures. Is this perhaps the largest prime yet discovered that we can't (yet) prove? It may well be (unless anyone knows any different?). It's what makes the better news headlines, isn't it? "We KNOW this 2 million+ digit number is prime!" (Oh, we're PRETTY SURE this similar- looking 86453-digit one is too). "We KNOW 5000 primes over 20,000 digits" (But we've been TRYING REAL HARD to factor 219 digits of 2^727-1, but no luck yet). Every once in a while, someone suggests Chris C.'s "5000 Largest Known Primes" ought to have a companion "Most Wanted" list of PRP's awaiting proof. (I suggest the PrimeForm files area!). Mentally I keep two such lists - the 'maybe one day soon' list, recently entered and exited by Phi(2521,402) - the 'no chance in he** list'. R(49081) bounced between the two for quite some time, I actually filled a lot of disk space with the current factor status of N-1 (a large, but relatively pitiful document). R(86453) surely has to go straight to #1 of the second list! Such a list would need some pretty stringent conditions on membership (more so than 'archivable forms' in the top 5000. There are evidently some PRP's that aren't worth the time spent looking for them, while others would be more important. Size isn't everything - but this one's miraculous. Chris

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