1.3063778838630806904...

This number is neither prime nor composite.

     1.306 3778838630 8069046861 4492602605 7129167845 8515671364 4368053759
9664340537 6682659882 1501403701 1973957072 9696093810 3086882238 8614478163
5348688713 3922146194 3534578711 0033188140 5093575355 8319326480 1721383236
1522359062 2186016108 5667905721 5197976095 1619929527 9707992563 1721527841
2371307658 4911245631 7518426331 0565215351 3186684155 0790793723 8592335220
8421842040 5320517689 0260257934 4300869529 0636205698 9687262122 7499787666
4385157661 9143877284 4982077590 5648255609 1500412378 8524793626 0880466881
5406437442 5340131073 6114409413 7650364379 3012676721 1713103026 5228386615
4666880487 4760951441 0790754069 8417260347 3107746775 7406400781 0935083421
4374426542 0408531116 5490420993 0908557470 5834879375 7769523336 3648583054
9292738728 1493416741 2502732669 2684046815 4062676311 3223748823 8001180412
0628601384 1914438857 1516091893 8894478991 2125543384 7493590927 4442208280
2260203323 0271063750 2228813106 4778444817 0037233364 0604211874 2608383328
2217696878 1235304962 3008802672 2111040160 6508880971 8347778314 0224908218
4410637749 4000232824 1927007123 3303228854 1285840889 1631372929 5257781669
7309365179 5130470139 3525757057 2884159917 3150678128 8275420005 4622901262
8840580670 1552761743 2706316257 0558788529 3887371663 6318690967 8515848077
1725887503 5917556106 5153430468 2508915720 5292189794 5191865689 6107079679
4540918003 9893947248 6242136261 0780178535 4328900449 9330170496 3668241389
9155939086 3407971519 5210549138 3217875024 8935369436 9110072710 3037261375
0972234285 3231161686 2854394418 8065497790 7392376187 0914189917 1623410941
6383085757 4665951481 4198482696 3646512305 8093661789 8571875292 5589242617
9224596035 6189889945 4332955343 9088187659 2175906931 3497049820 1200298150
8269262773 9578666580 3814559110 8464886110 4685164073 4818557724 3382358...

In the late forties Mills [Mills47] proved that there was a real number A>1 for which [] is always a prime (n = 1,2,3,...). This is (probably) one such value and is the number most often called Mills' constant. See our proof of Mills' Theorem. [Caldwell]