ANSWER: Part of your confusion regarding Islam is probably a result of how you define "nation." It is true that the Bible promises great nations to both Isaac and Ishmael, but what is a "nation"? In all but five instances in the Old Testament where the word "nation" is used, it is the Hebrew word goy, Strong's Concordance #1471, and means a Gentile or heathen nation or people.
Genesis 17 predicts two great nations coming from Abraham and Sarah in their old age. The first great nation sprang from Isaac, the only child born to Abraham and Sarah. The second nation would come from Ishmael, Abraham's first child through Hagar (Sarah's servant). It is through Abraham and Ishmael that Islam not only traces its roots but also considers itself an Abrahamic religion.
20 I have heard your request about Ishmael, so I will bless him and give him many children and many descendants. He will be the father of twelve princes, and I will make a great nation of his descendants (Genesis 17:20)
The twenty-fifth chapter of Genesis names the twelve princes of Ishmael and specifies where they lived. They were, in alphabetical order, Adbeel, Dumah, Hadar, Jetur, Kedar, Kedemah Massa, Mibsam, Mishma, Naphish, Nebajoth, and Tema. God's word states that they lived in Havilah as far as Shur, which is east of Egypt (see Genesis 25:12 - 18). One Scriptural dictionary had the following to say about Ishmael.
"The sons of Ishmael peopled the north and west of the Arabian peninsula and eventually formed the chief element of the Arab nation, the wandering Bedouin tribes."
Most of the Arab Bedouins recognize Muhammad (571 to 632 A.D.), who originated Islam, as their spiritual leader. This is why there is no mention of it in Holy Writ. Most references refer to them as Moslems, Mohammedans, or Muslims. Genesis 25:20 - 24 tells us that after Isaac and Rebekah married she conceived two children who would represent two nations. The older of the two children would ultimately serve the younger child.
The two nations in Rebekah's womb were the Edomites (through Esau, the older brother) and the Israelites (through Jacob, the younger brother). Most Christians in the world today are Israelites. If you study this religion, do it only as a means of comparison. There are vast differences in the two belief systems despite what you might hear to the contrary.
Facts about the religion
Adherents to Islam, which means 'submission to God,' are known as Muslims. Although the religion believes that Jesus was a prophet, it does NOT believe Jesus was the very SON OF GOD who came to earth to die for the world's sins. Most Muslims belong to one of two denominations, Sunni (80 - 90%) or Shia (10 - 20%). The largest Muslim country is Indonesia, where 13% of all Muslims in the world live.
Islam is the world's second largest religion, right behind Christianity (those who believe in the Bible). There are around 1.5 billion Muslims in the world, with roughly 2.5 million adherents in the United States of America. Those practicing the religion comprise about 22% of the world's population.