Let p1 = 2, p2 = 3, . . be the list of primes, in increasing order. consider products of the form (p1 × p2 × ·· ·× pn) + 1 (compare with the proof of corollary 1.3.4). show that this number is prime for n = 1, . . , 5. show that when n = 6 this number is not prime. [use your answer to exercise 1.3.1. a calculator will speed the work of checking divisibility.]

At steady state, air at 200 kpa, 325 k, and mass flow rate of 0.5 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. the inlet cross-sectional area is 6 cm2. at the duct exit, the pressure of the air is 100 kpa and the velocity is 250 m/s. neglecting potential energy effects and modeling air as an 1.008 kj/kg k, determine ideal gas with constant cp = (a) the velocity of the air at the inlet, in m/s. (b) the temperature of the air at the exit, in k. (c) the exit cross-sectional area, in cm2