In this article, we use set, function, sieve and number theory to study the prime and composite numbers, prove that the lower limit formula of the number of prime numbers derived from the Euler’s function, and find d(n) to count the lower limit formula of the number of prime integer-pairs. We proved that Goldbach’s conjecture is correct by mathematical induction. Finally, we proved proof reliance by mathematical analysis and computer data.

Abstract:
In this paper the progress in research and development of in ter metalliccompounds In briefly described.The characteristics of ordered alloys,especially thebrittleness problem and the way to overcome it,and the furture development trend are dis-cussed.

Abstract:
The effect of addition of Mg on the creep behaviour of Ni-base wrought superalloy has been investigated. It was found that the trace Mg added may cause the alteration of continueous lath carbide into discontinueous massive one at the grain boundaries. It may also promote the spheroidization of the grain boundary carbide, decrease the diffusion coefficient of grain boundary and increase the activation energy for creep. The grain boundary energy and the boundary energy between grain boundary carbide and matrix are decreased and bonding strength of interface increased. Thus, the creep property and the creep-rupture life as well as the stress exponent of creep of the superalloy may be significantly improved by the impediment of the boundary sliding and the prevention of the nucleation and propagation of cracks.

Abstract:
Beal conjecture is a famous world
mathematical problem and was proposed by American banker Beal, so to solve it is more
difficult than Fermat’s last theorem. This paper uses relationship between the mathematical formula and
corresponding graph, and by characteristics of graph, combined with the algebraic
transformation and congruence theory of number theory; it is proved that the equation can only be formed under having a common
factor and Beal conjecture is correct.

Abstract:
Two phases gamma titanium aluminide alloy,Ti-46.5Al-2.5V-1Cr.was investigated to characterizemicrostructures and to define the microstructure/mechanical property relationship.Many kinds ofmicrostructure of gamma and α_2 phases were obtained by heat treatments in the α+γ,α_2+γ and αfields.The effects of microstructure on tensile properties,fracture toughness and J-R resistancecurve at room temperature,were systematically studied.The experimental results showed that themicrostructure had a strong effect on mechanical properties,The duplex microstructure produced byheat treatment at 1250℃×4 h with controlled cooling resulted in the highest ductility of 4.8% tensileelongation,low fracture toughness and crack growth resistance.The fully lamellar microstructureproduced by heat treatment in the α field having large grain sizes resulted in the highest fracturetoughness but the lowest ductility.

Abstract:
The observations of the crack morpholgies on the side faces and fracture surfaces of the fracture toughness specimens and the TEM analyses of deformed structure around crack were conducted for the FFL microstructure which was obtained from the cast Ti-46.5 Al-2.5V-1.0Cr-0.2Ni(atomic fraction,%) alloy by a designed multiple heat treatment.The fracture characterizations of the FFL microstructure are similar to that of the FL microstructures.The functions of each shear ligment and total deformed volume accompanying the crack in the FFL microstructure were much smaller due to the significant decrease of the lamellar colony size.This led to a descent of fracture toughness of the FFL microstructure compared to the general FL microstructure.

Abstract:
A nuclear structure model
of “ring plus extra nucleon” is proposed. For nuclei larger than ^{4}He,
protons (P) and neutrons (N) are basically bound alternatively to form a ZP + ZN
ring. The ring folds with a “bond angle” of 90° for every 3 continuous nucleons
to make the nucleons packed densely. Extra N(‘s) can bind to ring-P with the
same “bond angle” and “bond distance”. When 2 or more P’s are geometrically
available, the extra N tends to be stable. Extra P can bind with ring N in a
similar way when the ratio of N/P < 1 although the binding is weaker than
that of extra N. Even-Z rings, as
well as normal even-even nuclei, always have superimposed gravity centers of P
and N; while for odd-Z rings, as well
as all odd-A (A: number of nucleon) nuclei, the centers of P and N must be
eccentric. The eccentricity results in a depression of binding energy (E_{B}) and therefore odd and
even Z dependent zigzag features of E_{B}/A. This can be well explained by the shift of eccentricity by extra
nucleons. Symmetrical center may present in even-Z rings and normal even-even nuclei. While for odd-Z ring, only antisymmetric center
(every P can find an N through the center and vice versa) is possible. Based on this model, a pair of mirror
nuclei, P_{X}_{+n}N_{X} and P_{X}N_{X}_{+n}, should be equivalent in packing structure just like
black-white photo and the negative film. Therefore, an identical spin and
parity was confirmed for any pair. In addition, the E_{B}/A difference of mirror nuclei pair is nearly a constant of 0.184n MeV. Many other facts can also be
easily understood from this model, such as the neutron halo, the unusual stability
sequence of ^{9}Be, ^{7}Be and ^{8}Be and so on.

Abstract:
The effect of coating of pure aluminum on the superplasticity of isothermally forged TiAl alloy is studied by tension experiments of plate specimen at high temperatures. It is found that the superplasticity of TiAl alloy will greatly increase when the sur

Abstract:
In the light of the valence electron structures and bond energy calculated by the empirical electron theory of solids and molecules(E.E.T),the relationship of embrittlement with the bond structures and electron distributions in Fe3Al and FeAl intermetalli