#problem 7 prime = [2,3] while(len(prime)<10001): # generate next prime check = 0 tmp = prime[len(prime)-1] # innit tmp while(check == 0): # get latest prime + 2 = tmp vi cac so prime con lai phai la so le tmp = tmp + 2 # kiem tra tmp is prime #input = list(range(2,tmp)) input = prime is_prime = 0 for i in input: if(tmp%i == 0): is_prime = 1 break # neu chia het 1 so trong prime thi thoat ra ko can kiem tra tiep if(is_prime == 0): prime.append(tmp) # them prime moi vao list check = 1 # thoat khoi vong lap print(prime[-1:])

# Project Euler #problem 2 fibo = [1,2] tong = 2 tong_cuoi = 0 while tong < 4000000: tmp = fibo[len(fibo)-1] + fibo[len(fibo)-2] fibo.append(tmp) tong = tmp for i in range(0,len(fibo)-1): if((fibo[i]%2)==0): tong_cuoi = tong_cuoi + fibo[i] print(fibo[i]) print(tong_cuoi) # Project Euler #problem 3 a = 600851475143 # number u need b = 2 # first prime factor c = 0 # max prime factor while a > 1: if(a%b == 0): a = a/b c = b else: b = b + 1 print(c) # Project Euler #problem 4 a = list(range(100,1000)) b = list(range(100,1000)) current_max = 0 for i in range(len(a)-1,-1,-1): for j in range(len(b)-1,-1,-1): current_max = a[i] * b[j] if current_max > 900000: tmp = str(current_max) if(tmp[0] == tmp[5]) and (tmp[1] == tmp[4]) and (tmp[2] == tmp[3]) : print(str(a[i]) + ' * ' + str(b[j]) + ' = ' + str(current_max)) break ## second approach pal = [] numbers = list(range(100,998002)) for i in numbers: tmp = str(i) if(len(tmp) == 6): if(tmp[0] == tmp[5]) and (tmp[1] == tmp[4]) and (tmp[2] == tmp[3]): pal.append(i) solonnhat = 0 so1 = 0 so2 = 0 for p in pal: for j in range(1000,1,-1): if(p%j == 0) and (len(str(j)) == 3) and (len(str(int(p/j))) == 3): solonnhat = p so1 = j so2 = p/j #print(str(j)+ ' * '+str(p/j) + ' = ' + str(p)) break print(str(so1)+ ' * '+str(so2) + ' = ' + str(solonnhat)) ## problem 4 input = list(range(1,21)) print(input) #1 - tim tat ca so nguyen to trong day result = [] for i in input: check = 0 for j in range(2,i): if(i%j == 0): check = check + 1 if(check == 0): result.append(i) result.remove(1) print(result) #2 - tim so nguyen to sao cho mu n < so lon nhat trong day power = [] for i in result: for j in input: if(pow(i,j)>20): power.append(j-1) break print(power) #3 - tinh tich cac ket qua tren bcnn = 1 for i in range(0,len(result)): tmp = pow(result[i],power[i]) bcnn = bcnn * tmp print(bcnn) #problem 6 sum_square = 0 square_sum = 0 for i in range(1,101): sum_square = sum_square + (i*i) square_sum = square_sum + i print(square_sum * square_sum - sum_square)

#problem 8 numbers = '''7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450''' input = [] for i in range(0,len(numbers)-1): x = list(numbers[i:i+13]) y = [] check_0 = 0 # neu trong chuoi co so 1 va 0 thi tich cua chuoi do se ko phai la tich so lon nhat for i in x: if int(i) in (0,1): check_0 = 1 y.append(int(i)) # Neu trong chuoi ko chua 1 va 0 thi them list nay vao mang input if check_0 == 0 : input.append(y) print(input) print(y) # chuoi co tich so lon nhat cung la chuoi co tong cac chu so lon nhat sum_d = [] for i in range(0,len(input)-1): tmp_sum = sum(input[i]) sum_d.append( tmp_sum) print(sum_d) for i in range(0,len(sum_d)-1): if((sum_d[i]) == max(sum_d)): print('%s : %s' %(i,sum_d[i])) print(input[9]) tmp_sum = 1 for i in input[9]: tmp_sum = tmp_sum * i print(tmp_sum)

#problem 9 # all possible pytago triple - if (a,b,c) is pytago triple then k(a,b,c) is pytago triple too triple = [ [3, 4, 5], [5, 12, 13], [7, 24, 25], [8, 15, 17], [9, 40, 41], [11, 60, 61], [12, 35, 37], [13, 84, 85], [16, 63, 65], [20, 21, 29], [28, 45, 53], [33, 56, 65], [36, 77, 85], [39, 80, 89], [48, 55, 73], [65, 72, 97] ] for i in triple : check = False if ( 1000%sum(i) == 0): check = True print(i) break print('%d : %d : %d'%((8*25),(15*25),(17*25))) print('a*b*c = %d'%(200*375*425))

#problem 10 # generate list of prime < n def sieve(n): "Return all primes <= n." np1 = n + 1 s = list(range(np1)) # leave off `list()` in Python 2 s[1] = 0 sqrtn = int(round(n**0.5)) for i in range(2, sqrtn + 1): # use `xrange()` in Python 2 if s[i]: # next line: use `xrange()` in Python 2 s[i*i: np1: i] = [0] * len(range(i*i, np1, i)) result = [x for x in s if x >0 ] return result a = sieve(2000000) print(sum(a)) #problem 13 li_input = [37107287533902102798797998220837590246510135740250, 46376937677490009712648124896970078050417018260538, 74324986199524741059474233309513058123726617309629, 91942213363574161572522430563301811072406154908250, 23067588207539346171171980310421047513778063246676, 89261670696623633820136378418383684178734361726757, 28112879812849979408065481931592621691275889832738, 44274228917432520321923589422876796487670272189318, 47451445736001306439091167216856844588711603153276, 70386486105843025439939619828917593665686757934951, 62176457141856560629502157223196586755079324193331, 64906352462741904929101432445813822663347944758178, 92575867718337217661963751590579239728245598838407, 58203565325359399008402633568948830189458628227828, 80181199384826282014278194139940567587151170094390, 35398664372827112653829987240784473053190104293586, 86515506006295864861532075273371959191420517255829, 71693888707715466499115593487603532921714970056938, 54370070576826684624621495650076471787294438377604, 53282654108756828443191190634694037855217779295145, 36123272525000296071075082563815656710885258350721, 45876576172410976447339110607218265236877223636045, 17423706905851860660448207621209813287860733969412, 81142660418086830619328460811191061556940512689692, 51934325451728388641918047049293215058642563049483, 62467221648435076201727918039944693004732956340691, 15732444386908125794514089057706229429197107928209, 55037687525678773091862540744969844508330393682126, 18336384825330154686196124348767681297534375946515, 80386287592878490201521685554828717201219257766954, 78182833757993103614740356856449095527097864797581, 16726320100436897842553539920931837441497806860984, 48403098129077791799088218795327364475675590848030, 87086987551392711854517078544161852424320693150332, 59959406895756536782107074926966537676326235447210, 69793950679652694742597709739166693763042633987085, 41052684708299085211399427365734116182760315001271, 65378607361501080857009149939512557028198746004375, 35829035317434717326932123578154982629742552737307, 94953759765105305946966067683156574377167401875275, 88902802571733229619176668713819931811048770190271, 25267680276078003013678680992525463401061632866526, 36270218540497705585629946580636237993140746255962, 24074486908231174977792365466257246923322810917141, 91430288197103288597806669760892938638285025333403, 34413065578016127815921815005561868836468420090470, 23053081172816430487623791969842487255036638784583, 11487696932154902810424020138335124462181441773470, 63783299490636259666498587618221225225512486764533, 67720186971698544312419572409913959008952310058822, 95548255300263520781532296796249481641953868218774, 76085327132285723110424803456124867697064507995236, 37774242535411291684276865538926205024910326572967, 23701913275725675285653248258265463092207058596522, 29798860272258331913126375147341994889534765745501, 18495701454879288984856827726077713721403798879715, 38298203783031473527721580348144513491373226651381, 34829543829199918180278916522431027392251122869539, 40957953066405232632538044100059654939159879593635, 29746152185502371307642255121183693803580388584903, 41698116222072977186158236678424689157993532961922, 62467957194401269043877107275048102390895523597457, 23189706772547915061505504953922979530901129967519, 86188088225875314529584099251203829009407770775672, 11306739708304724483816533873502340845647058077308, 82959174767140363198008187129011875491310547126581, 97623331044818386269515456334926366572897563400500, 42846280183517070527831839425882145521227251250327, 55121603546981200581762165212827652751691296897789, 32238195734329339946437501907836945765883352399886, 75506164965184775180738168837861091527357929701337, 62177842752192623401942399639168044983993173312731, 32924185707147349566916674687634660915035914677504, 99518671430235219628894890102423325116913619626622, 73267460800591547471830798392868535206946944540724, 76841822524674417161514036427982273348055556214818, 97142617910342598647204516893989422179826088076852, 87783646182799346313767754307809363333018982642090, 10848802521674670883215120185883543223812876952786, 71329612474782464538636993009049310363619763878039, 62184073572399794223406235393808339651327408011116, 66627891981488087797941876876144230030984490851411, 60661826293682836764744779239180335110989069790714, 85786944089552990653640447425576083659976645795096, 66024396409905389607120198219976047599490197230297, 64913982680032973156037120041377903785566085089252, 16730939319872750275468906903707539413042652315011, 94809377245048795150954100921645863754710598436791, 78639167021187492431995700641917969777599028300699, 15368713711936614952811305876380278410754449733078, 40789923115535562561142322423255033685442488917353, 44889911501440648020369068063960672322193204149535, 41503128880339536053299340368006977710650566631954, 81234880673210146739058568557934581403627822703280, 82616570773948327592232845941706525094512325230608, 22918802058777319719839450180888072429661980811197, 77158542502016545090413245809786882778948721859617, 72107838435069186155435662884062257473692284509516, 20849603980134001723930671666823555245252804609722, 53503534226472524250874054075591789781264330331690] tmp_sum = str(sum(li_input)) sum_r = '' for i in range(0,11): sum_r += (tmp_sum[i]) print(sum(li_input)) print(sum_r) #problem 14 def even(n): global count count+=1 return int(n/2) def odd(n): global count count+=1 return 3*n+1 l ={} for n in range(1,1000001): count = 1 x = n while(x!=1): if x in l: count+= l[x]-1 break if(x%2 == 0): x =even(x) else: x =odd(x) l[n] = count keys = list(l.keys()) values = list(l.values()) index = values.index(max(values)) print(keys[index])