On Fri, 20 Dec 2002, Richard Guy wrote:

I think that I have upped this to 10^64, and someone who knew how to sieve could probably go much further. It's a probably fruitless task, but one admits to being tantalized by u_n - u_37 =

919p for n = 144 5p 234 79p 264 9349p 306

Of course, those pees are industrial strength, but there's no doubt that the small factors are OK. R.

On Fri, 20 Dec 2002, Neil Fernandez wrote:

...

2,3,29,199,2351,24155233, next term >10^15

a(n) = smallest prime > a(n-1) such that sum of first n terms is a Fibonacci number

a(7), if it exists, > 10^15

Neil -- Neil Fernandez

Using Maple 8's isprime and fibonacci procedures I found quickly a(7),a(8),a(9) and a(10): a(7) = 7975700805764462335030007876480792371250913910303944841855325915515983 3055572871 a(8) = 3668447431608097806147361364627563045102082989313758519191994278965296 0137481051718801295569460987256072983944701335181 a(9) = 2860237443871101020092695809288461418226282996794086786910075167259268 7035109337095292097358449707276902123226375514620345724087195622144641 6410838906931754749275206157126901576731550774066285780641215850983247 2455863450508771548297024385499680217193918846988297841120317579666235 7717188112967384947822225345517847656126062020335112736501648910321467 0033556109094154697008792681257572275338612132452049497949325037206499 8506512506621603628523778890116919873134761960331838056827741029556206 7370068703392922220614491028403281979478507933216420429100210102893565 56387551924106451 a(10) = 7027718237827374688136625495531694276786981404535405760355985679270119 0299810437666011816928553796869241163173859857185970291171314598486495 8896484231945630144368935219205138453121755856290611129068491630157461 7061509923368356607854862812379742674999040025587846722257561980277819 4836981892398204559957049399940416576881959655919881463509220091089992 5185603881956954829912396329901052508322013568031969237222342685812555 7180702466596350263451550719141076480839197607120839271866804594223176 1732815196072335821230739952542624915991003126789153623240195594308057 2977775604699655600788376503487234434288968113706492318041348901212028 4696120487246606478185429112993860835587883784462070881493 E.C.