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By Armand Borel

Half 1 includes sections on Reductive teams, representations, Automorphic varieties and representations)

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Smith, J. Smith & S. Zarantonello. D. H. Lehmer puts 8 1 = 4, 8k+1 = 8~ - 2, supposes that 2P - 1 is a Mersenne prime, notes that 8 p - 2 == 2(p+1)/2 or _2(p+1)/2 mod 2P - 1 and asks: which? Selfridge observes that the problem was asked in 1954 by Raphael Robinson. In a 94-06-22 email, Franz Lemmermeier provides much evidence, later further strengthened by Robert Harley, that if 2P - 1 is written in the form 4a 2 + 27b2 , then the sign is that of the Jacobi symbol (~) (see F5). Sun Zhi-Hong had made a similar conjecture on 88-09-19.

Renyi, Some problems and results on consecutive primes, Simon Stevin, 27(1950) 115-125; MR 11, 644. M. F. Jones, M. Lal & W. J. Blundon, Statistics on certain large primes, Math. , 21(1967) 103-107; MR 36 #3707. L. J. Lander & T. R. Parkin, Consecutive primes in arithmetic progression, Math. , 21(1967) 489. H. L. Nelson, There is a better sequence, J. , 8(1975) 39-43. Unsolved Problems in Number Theory 30 s. Weintraub, Consectutive primes in arithmetic progression, J. , 25(1993) 169-17l. OEIS: A031217.

Chen Jing-Run, On the least prime in an arithmetical progression and two theorems concerning the zeros of Dirichlet's L-functions, Sci. Sinica, 20(1977) 529-562; MR 57 #16227. 24 Unsolved Problems in Number Theory Chen Jing-Run, On the least prime in an arithmetical progression and theorems concerning the zeros of Dirichlet's L-functions II, Sci. Sinica, 22(1979) 859-889; MR 80k:10042. Chen Jing-Run & Liu Jian-Min, On the least prime in an arithmetic progression III, IV, Sci. China Ser. A, 32(1989) 654-673, 792-807; MR 91h:11090ab.

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