2018-09-24-154558.sagews

n = 0  #where n starts
# a, b, and c are the coefficients for an^2+bn+c
a = 1
b = -79
c = 1601
k = 100  # range to check, where n ends
count = 0 # count of non-prime results between primes

print(" n -  Fn   - Count")
for n in range(k):
    solution = a*n^2 + b*n +c
    if is_prime(solution):
        print("{:2d} {:6d} {:6d}".format(n,solution,count))
        count = 0
        #print("{}{}".format(solution,"&")) #this is for copy/paste for tables in LaTex
    else:
        count += 1
        print("{:2d} {:>6s} {:6d}".format(n, "No",count))
        #print("No&") #this is for copy/paste for tables in LaTex

n - Fn - Count 0 1601 0 1 1523 0 2 1447 0 3 1373 0 4 1301 0 5 1231 0 6 1163 0 7 1097 0 8 1033 0 9 971 0 10 911 0 11 853 0 12 797 0 13 743 0 14 691 0 15 641 0 16 593 0 17 547 0 18 503 0 19 461 0 20 421 0 21 383 0 22 347 0 23 313 0 24 281 0 25 251 0 26 223 0 27 197 0 28 173 0 29 151 0 30 131 0 31 113 0 32 97 0 33 83 0 34 71 0 35 61 0 36 53 0 37 47 0 38 43 0 39 41 0 40 41 0 41 43 0 42 47 0 43 53 0 44 61 0 45 71 0 46 83 0 47 97 0 48 113 0 49 131 0 50 151 0 51 173 0 52 197 0 53 223 0 54 251 0 55 281 0 56 313 0 57 347 0 58 383 0 59 421 0 60 461 0 61 503 0 62 547 0 63 593 0 64 641 0 65 691 0 66 743 0 67 797 0 68 853 0 69 911 0 70 971 0 71 1033 0 72 1097 0 73 1163 0 74 1231 0 75 1301 0 76 1373 0 77 1447 0 78 1523 0 79 1601 0 80 No 1 81 No 2 82 1847 2 83 1933 0 84 No 1 85 2111 1 86 2203 0 87 2297 0 88 2393 0 89 No 1 90 2591 1 91 2693 0 92 2797 0 93 2903 0 94 3011 0 95 3121 0 96 No 1 97 3347 1 98 3463 0 99 3581 0

list =[]

for n in range(k):
    solution = a*n^2 + b*n +c
    if is_prime(solution):
        list.append((n,solution))
    else:
        list.append((n,0))
print(list)

[(0, 1601), (1, 1523), (2, 1447), (3, 1373), (4, 1301), (5, 1231), (6, 1163), (7, 1097), (8, 1033), (9, 971), (10, 911), (11, 853), (12, 797), (13, 743), (14, 691), (15, 641), (16, 593), (17, 547), (18, 503), (19, 461), (20, 421), (21, 383), (22, 347), (23, 313), (24, 281), (25, 251), (26, 223), (27, 197), (28, 173), (29, 151), (30, 131), (31, 113), (32, 97), (33, 83), (34, 71), (35, 61), (36, 53), (37, 47), (38, 43), (39, 41), (40, 41), (41, 43), (42, 47), (43, 53), (44, 61), (45, 71), (46, 83), (47, 97), (48, 113), (49, 131), (50, 151), (51, 173), (52, 197), (53, 223), (54, 251), (55, 281), (56, 313), (57, 347), (58, 383), (59, 421), (60, 461), (61, 503), (62, 547), (63, 593), (64, 641), (65, 691), (66, 743), (67, 797), (68, 853), (69, 911), (70, 971), (71, 1033), (72, 1097), (73, 1163), (74, 1231), (75, 1301), (76, 1373), (77, 1447), (78, 1523), (79, 1601), (80, 0), (81, 0), (82, 1847), (83, 1933), (84, 0), (85, 2111), (86, 2203), (87, 2297), (88, 2393), (89, 0), (90, 2591), (91, 2693), (92, 2797), (93, 2903), (94, 3011), (95, 3121), (96, 0), (97, 3347), (98, 3463), (99, 3581)]

scatter_plot(list)

n = 0  #where n starts
# a, b, and c are the coefficients for an^2+bn+c
a = 1
b = -79
c = 1601
k = 100  # range to check, where n ends
count = 0 # count of non-prime results between primes
countList = []
for n in range(k):
    solution = a*n^2 + b*n +c
    if is_prime(solution):
        countList.append((n,count))
        count = 0
    else:
        count += 1
        countList.append((n,count))
print(countList)

[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (8, 0), (9, 0), (10, 0), (11, 0), (12, 0), (13, 0), (14, 0), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0), (21, 0), (22, 0), (23, 0), (24, 0), (25, 0), (26, 0), (27, 0), (28, 0), (29, 0), (30, 0), (31, 0), (32, 0), (33, 0), (34, 0), (35, 0), (36, 0), (37, 0), (38, 0), (39, 0), (40, 0), (41, 0), (42, 0), (43, 0), (44, 0), (45, 0), (46, 0), (47, 0), (48, 0), (49, 0), (50, 0), (51, 0), (52, 0), (53, 0), (54, 0), (55, 0), (56, 0), (57, 0), (58, 0), (59, 0), (60, 0), (61, 0), (62, 0), (63, 0), (64, 0), (65, 0), (66, 0), (67, 0), (68, 0), (69, 0), (70, 0), (71, 0), (72, 0), (73, 0), (74, 0), (75, 0), (76, 0), (77, 0), (78, 0), (79, 0), (80, 1), (81, 2), (82, 2), (83, 0), (84, 1), (85, 1), (86, 0), (87, 0), (88, 0), (89, 1), (90, 1), (91, 0), (92, 0), (93, 0), (94, 0), (95, 0), (96, 1), (97, 1), (98, 0), (99, 0)] done1

scatter_plot(countList)