When n = 1,2,3,4,5, is the value of the algebraic formula n & sup2; - 3N + 7 prime? Are you sure that for all natural numbers, the value of the formula n & sup2; - 3N + 7 is prime?

When n = 1,2,3,4,5, is the value of the algebraic formula n & sup2; - 3N + 7 prime? Are you sure that for all natural numbers, the value of the formula n & sup2; - 3N + 7 is prime?

Substituting n = 1,2,3,4,5 into n & sup2; - 3N + 7 respectively;
When n = 1, n & sup2; - 3N + 7 = 5
n＝2,n²－3n＋7＝5
n＝3,n²－3n＋7＝7
n＝4,n²－3n＋7＝11
n＝5,n²－3n＋7＝17
5. 5, 7, 11 and 17 are prime numbers
Natural numbers are only 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
n²－3n+7
The original formula = (n & sup2; - 3N + 2) + 5
＝（n－1）（n－2）＋5
The value of (n-1) (n-2) must be a composite number
The composite number + 5 is not necessarily prime
For all natural numbers, the value of the formula n & sup2; - 3N + 7 is not necessarily prime
If n = 6, n & sup2; - 3N + 7 = 25, 25 = 5 × 5 is a composite number
That's it,

A second grade math problem, homework, master quickly
As shown in the figure, △ ABO, Ao = Bo and Ao ⊥ Bo, take the midpoint P of ab. if ∠ rpq = 45 °, PR intersects OA at R, PQ intersects OA at Q, the extension line of intersection Bo is at point G, connected with gr. prove: RG = Ar + go

Remember one thing: since we want to prove RG = Ar + go, we need to get RG = a certain edge in a triangle. From the meaning of the question, we can find a point R "making RG = GR" on Bo. We can prove it with this clue. I hope you can answer it

A company designed a handicraft with a cost of 20 yuan and put it on the market. After investigation, the following data are obtained
Sales unit price x (yuan / piece) 30 40 50 60
Daily sales volume y (pieces) 500 400 300 200
(1) Finding the function analytic expression of Y and X
(2) When the sales unit price is, the craft factory will get the biggest profit by dumping the craft. What's the biggest profit? I listed the profit = (- 10x + 800) times (x-20), but when I don't know the value of X, the profit will be the biggest. Please write down the problem-solving process
(3) According to the local price department, the highest selling price of the handicraft can't exceed 45 yuan / piece. When the selling unit price is fixed, the factory will get the biggest profit from the trial sale of the handicraft

(1) Let the analytic formula be ax + by = C, substituting X and Y into a = 10, B = 1, C = 800 respectively, that is, 10x + y = 800 is the analytic formula. (2) let profit be p, then profit P = y (x-20), bring in y = 800-10x to get P = - 10 (x * X-60 + 1600)