diff --git a/euclid.py b/euclid.py
index da5c4aa..23e54a9 100644
--- a/euclid.py
+++ b/euclid.py
@@ -2,3 +2,20 @@
 b = input("b の値を入力: ")
 
 # TODO
+def gcd(a,b):
+    while b != 0:
+        a,b = b, int(a) % int(b)
+    return a 
+result3 = gcd(a,b)
+print(result3)
+
+def coprime(a,b):
+    while b != 0:
+        a,b = b, int(a) % int(b)
+    return a == 1
+
+result4 = coprime(a,b)
+if result4:
+    print(f"{a}と{b}は互いに素")
+else:
+    print(f"{a}と{b}は互いに素ではない")
diff --git a/machine_epsilon.py b/machine_epsilon.py
index f87f5c1..ff2b6a3 100644
--- a/machine_epsilon.py
+++ b/machine_epsilon.py
@@ -1 +1,5 @@
-# TODO
\ No newline at end of file
+# TODO
+epsilon = 1
+while 1 + epsilon > 1:
+    epsilon = epsilon/2
+print(epsilon)
\ No newline at end of file
diff --git a/prime_number.py b/prime_number.py
index 2308cf4..98b19e7 100644
--- a/prime_number.py
+++ b/prime_number.py
@@ -1,4 +1,23 @@
 a = input("aの値を入力: ")
 b = input("bの値を入力: ")
 
-# TODO
\ No newline at end of file
+# TODO
+def check_natural(n):
+    if not n.isdigit() or int(n)<0:
+        raise ValueError('{}は自然数ではありません'.format(n))
+check_natural(a)
+check_natural(b)
+
+def is_prime(n):
+    if int(n) < 2:
+        return False
+    for i in range(2,int(n)):
+        if int(n) % i == 0:
+            return False
+    return True
+
+for x in [a,b]:
+    if is_prime(x):
+        print('{}は素数'.format(x))
+    else:
+        print('{}は素数ではない'.format(x))
\ No newline at end of file
diff --git a/trapezoidal_integral.py b/trapezoidal_integral.py
index 716aa70..2dd455d 100644
--- a/trapezoidal_integral.py
+++ b/trapezoidal_integral.py
@@ -3,3 +3,40 @@
 # print(sin(0))
 # >>> 0
 # -----------
+from math import pi
+
+def integral(f,a=0,b=1,n=100):
+    S=0
+    h = (b - a)/n
+    for i in range(1,n+1):
+        S += h/2 * (f(a + (i-1)*h)+f(a+i*h))
+    return (S)
+
+result1 = integral(sin,0,pi/2,50)
+print('(1){}'.format(result1))
+
+def func2(x):
+    return 4/(1+x**2)
+
+result2 = integral(func2)
+print('(2){}'.format(result2))
+
+from math import sqrt
+from math import exp
+def func3(x):
+    return sqrt(pi)*exp(-x)
+
+result3 = integral(func3,-100,100,1000)
+print('(3){}'.format(result3))
+
+
+    
+
+
+
+
+
+
+
+
+