A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself, like 2, 3, 5, and 7. They are unique because they can’t be broken down into smaller factors, unlike other numbers.
Prime numbers are valuable for more than just their uniqueness. For example, they are crucial to cryptography, which keeps digital systems secure. Very large numbers with large prime factors are especially useful because they’re hard to factorise (that is, to find the prime factors). Many digital security systems, such as those protecting online banking and private messaging, rely on this difficulty. These systems multiply two large prime numbers to create an even larger number, forming part of the “key” that secures information. Since breaking this number down into its original primes is so complex, unauthorized parties cannot easily intercept and read secure messages without the proper key.
Given the critical role of prime numbers in securing information in today’s digital world, the recent discovery of the largest-ever is noteworthy. In theory, larger prime numbers mean stronger cryptographic potential and more secure systems.
Luke Durant, a 36-year-old researcher and former NVIDIA employee, identified this newest number using the Great Internet Mersenne Prime Search (GIMPS), a free programme available to the public. He used an advanced algorithm to make the discovery. A Mersenne prime is a prime number that can be expressed in the form Mn = 2n-1. The first eight Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, and 2147483647.
The newly discovered prime, now the largest known, is 2136,279,841-1, having 41,024,320 decimal digits. The find was far from a pen-and-paper calculation or a single-PC task; Durant required thousands of GPUs across 24 data centres in 17 countries. After a year of testing, he identified the number on October 11, 2024, marking a monumental achievement and highlighting why discoveries of new large prime numbers are so rare.
While this is an exciting breakthrough, the researchers acknowledge that Mersenne primes currently have few practical applications, particularly in cryptography, ironically. Due to their rarity and the fact they are well-documented, they are not ideal for encryption as they would be relatively easy to guess. Nonetheless, this discovery pushes the boundaries of number theory and computing power, setting a new milestone in the search for ever-larger prime numbers.
If you are interested n studying Maths, Oxford Open Learning offer the chance to do so at several levels, listed below. You can also Contact Us.
Maths GCSE and IGCSE Fast Track
Algorithms are everywhere in our digital landscapes and play an important part in our everyday experiences, whether it’s the social content we see or the products we’re shopping for. To enable this, many complex calculations are made using vast amounts of data to offer us personalised experiences based on our preferences and online habits.
Creators of algorithms can take inspiration from many sources. Google’s search engine algorithm ‘PageRank’, for example, was inspired by the principle of academic citations. Using the approach to rank websites by how many other sites link to it has made PageRank one of the most successful algorithms in the world.
Algorithms help deliver tailored, personalised content. By collecting information on user online interactions such as clicks, read content, location and browsing history, algorithms can create a user profile to help predict the type of content a user would be interested in. They process large amounts of data to do this, and can even use a technique called collaborative filtering, offering content based on similar user profiles.
Popular platforms that utilise these techniques include social media platforms, which decide which posts and videos to show to keep a user engaged based on their previous interactions and views. Streaming platforms suggest new films or music based on past consumption, previous ratings and genres that fit the user profile. The use of algorithms are also highly popular in the field of targeted advertising and e-commerce.
Algorithms have a significant impact on public perceptions and in areas such as politics. They can contribute to the creation of echo chambers, recommending content similar to what users have already interacted with, reinforcing pre-existing views and beliefs. Over time, this effect can lead to polarisation, where users are less likely to be exposed to opposing perspectives, thereby developing more extreme viewpoints. In the case of political campaigns, microtargeting can be used to target voters with highly specific messaging.
As algorithms become more integrated into our everyday life, so does their ethical concern. The training algorithms receive can incorporate biases into their programming that can lead to discrimination and the promotion of inequality. Due to the large amount of self-learning and governance that algorithms have, there is often a lack of transparency or understanding on how they arrived at their decisions. There is also the issue of data privacy that arises from the vast amounts of personal data collected.
There are, however, large benefits to the use of algorithms and it’s expected that the future will bring with it increasingly personalised experiences, ethical auditing, job automation. Future algorithms developments are also expected to increase productivity and provide substantial benefits to many industries such as medicine, transport and finance.
If you are interested in studying Maths, Oxford Open Learning offer the chance to do so at several levels, listed below. You can also Contact Us.
The Monty Hall Problem has baffled mathematicians, statisticians and people alike, not because of its complexity, but due to its counterintuitive solution. The problem has sparked debates for decades, gaining widespread popularity after being discussed in a column by Marylin vos Savant in Parade magazine in 1990. The Monty Hall Problem challenges our instincts about probability and our rational reasoning behind it.
The Monty Hall Problem comes from the gameshow Let’s Make a Deal and is named after the gameshow host, Monty Hall. During the show, contestants are presented with three doors: one with a hidden car prize and the other two concealing goats. They are then asked to pick the door they think the car is behind. Once chosen, Monty Hall, knowing which door contains the car, will open one of the other two remaining doors always containing a goat. The contestant is then given the choice to stick with their original choice or switch. Statistically, you will always have a higher chance of winning if you switch.
The explanation to the Monty Hall Problem reveals why switching is better but may still not be easily accepted by our rational and logical selves. When a contestant makes their original choice, they have a 1/3 chance of picking the car and a 2/3 chance of choosing a goat. Once Monty then opens a remaining door to reveal a goat, the initial choice (which was 2/3 likely to be a goat at the time) will have better odds by switching to the other remaining door (which now has an increased 2/3 probability of being the car).
The Monty Hall Problem reveals interesting insights into human decision making and cognitive biases that can lead to errors in our judgement. Many people incorrectly believe that once Monty reveals a goat, the probability of picking a car from the last two doors is 50/50 and don’t think that switching makes a difference to their chances.
Within educational settings, the problem helps inform us how strong our biases can be, even when presented with clear, contradictory facts, allowing students to hold discussions and debate their innate decision-making processes. Cognitive biases affect our everyday decision making, from personal relationships to challenges in work, where we often have to make decisions based on incomplete information. Re-assessing business negations based on new information, for example, could lead to better outcomes.
If you are interested in studying Maths or Psychology, Oxford Open Learning offer the chance to do so at several levels, listed below. You can also Contact Us.
To mark International Women in Engineering Day on the 23rd June, let’s shine a light on some of the best and brightest female engineers to have influenced the history of Britain.
Ada was born in London in 1815. Her mother was a mathematician and so Ada developed a love of maths and science from a young age. She studied under mathematician Charles Babbage whilst he worked on a prototype for an early computer called the Analytical Engine. Ada’s work on the Analytical Engine, for which she developed the first example of a computer programme, is her most notable contribution to computer science.
Born in 1833, Henrietta grew up in poverty and was largely a self-taught engineer and inventor who was likely inspired and educated by her blacksmith-inventor father, James Lowe. James had invented a screw propeller, but this invention had limited success. After her father’s death in 1866, Henrietta continued his work, further developing the screw propeller and obtaining British and US patents in her name. Henrietta’s screw propeller was far more successful than her father’s original invention. It was used on numerous naval and civic ships, allowing them to move faster and more efficiently in the water, and gained her several national and international engineering awards.
The wife of fellow engineer Charles Parsons, Katharine (pictured) is known for leading the Women’s Engineering Society in the early 20th century. Katharine was born in Yorkshire in 1858 and began taking an interest in her husband’s engineering projects shortly after the pair married in 1882. The couple spent much time developing steam turbines in the late 1800s. During the First World War, Katharine managed a team of women in an armament factory and, in 1919, was elected Fellow of the Institution of Engineers and Shipbuilders in recognition of her contribution to the field.
Beatrice was born in 1909 and demonstrated an interest in mechanics from an early age. After leaving school in 1926, she became an apprentice at an electrical engineering company run by one of the co-founders of the Women’s Engineering Society. Beatrice later went on to study at the University of Manchester where she gained a Bachelor’s degree in electrical engineering and a Master’s in mechanical engineering. In 1936, after her first role as a research assistant on aircraft engines, she gained a post at the Royal Aircraft Establishment where she was responsible for the adaptation of an aircraft engine which ultimately gave the Royal Air Force a significant advantage during the Second World War.
Scientist Rosalind Franklin is well known for the hugely significant contributions she has made to our understanding of molecular biology and genetics. She was born in London in 1920 and, as a young woman, gained a degree and doctorate in chemistry from Cambridge University. Her most notable work was the study of the structure of DNA through the use of X-ray crystallography.
For information about more female engineers, visit Top 100 Women in Engineering – Magnificent Women.
If you are interested in studying Maths or a Science subject, Oxford Open Learning offers you the chance to do so at a number of levels, listed below. You can also Contact Us.
Human Biology Fast Track IGCSE
Maths Fast Track IGCSE and GCSE
The golden ratio, sometimes also called the divine proportion or golden mean, is a unique number that is predominantly found within mathematics, art and architecture. It has influenced everything from the structure of the pyramids, Beethoven’s music, da Vinci’s Mona Lisa, to the Fibonacci Sequence and urban design.
The origins of this equation can be traced back to around 300 BC Greece, where mathematicians such as Euclid and Pythagoras recognised its patterns and proportions and donated it the Greek letter Phi (φ). It was not until later that it gained publicity through the artwork of Leonardo da Vinci and published works by Pacioli in the 16th century.
It is believed the golden ratio is aesthetically pleasing because it occurs so ubiquitously in the natural world. This can be seen in the ‘golden spirals’ of nautilus shells and animal horns or the ratio of the human body, such as the position of the belly button and facial features. Plants that have adapted the use of the golden ratio grow leaves that hang in such a way as not to shade each other.
It has long been know that designs and paintings that adhere to the golden ratio have harmonious, appealing and balanced compositions. Many famous artistic pieces can be attributed to this rule, such as Leonardo da Vinci’s “The Last Supper” and “The Mona Lisa” and Vincent van Gogh’s “The Starry Night”. Mozart also arranged the number of musical bars in his piano sonatas to this divine ratio, as can be seen in his Piano Sonata No. 1 in C Major.
The golden ratio is a number that is equal to about 1.618. If we divide a line into two parts at the golden ratio (which is just under two thirds), the whole length divided by the longest part would be the same as the long part divided by the short part. The golden ratio is very close to the Fibonacci sequence – a sequence of numbers where each number is the sum of the two proceeding ones. As the sequence increases 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 etc the ratio between the numbers gets closer to the golden ratio.
Today, the golden ratio is used by many graphic designers and web developers to create visually pleasing layouts, logos and adverts that appeal to audiences. In the field of genetics, scientists have explored the connections between the golden ratio and genetic pattern in DNA strands, while in the field of AI, researchers are investigating the principles of golden ratio inspired algorithms and pattern recognition. It stands as a timeless, universal principle that, with further understanding, will deepen our knowledge of the world around us.
If you have an interest in studying Maths, Oxford Open Learning offers you the chance to do so at several levels, listed below. You can also Contact Us.
There is nothing scientific about my ranking system; I am featuring the equations that seem to have permeated the mainstream.
In terms of fame, there are three big equations, derived from Einstein, Pythagoras, and Newton. We are all exposed to these regularly through mainstream media and/or through secondary education. While Schrödinger’s Equation is not that well-known by the layperson, most of us have heard of the associated Schrödinger’s cat thought experiment which helps to explain the principles of quantum mechanics.
This equation has even made it onto T-shirts as some kind of nerdy fashion statement, so most people are aware of it, even if they don’t know what it means. Proposed by Albert Einstein, perhaps the most famous scientist in history, it’s no surprise this E = mc² is the most well-known, but one of the least understandable to the layman. The answer? In short, Einstein showed that a small amount of mass can create a heck of a lot of energy – as in the amount you find in in stars – and it paved the way to the nuclear age.
We all did this at school so it’s one’s pretty famous and is attributed to the ancient Greek mathematician Pythagoras. It states that for any triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem forms the basis of Euclidean geometry which is used in architecture and navigation.
Formulated by Sir Isaac Newton, and popularised by the scientist’s apple falling on head Eureka moment, this equation describes the relationship between force (F), mass (m), and acceleration (a). The first states that an object’s motion will not change unless acted upon by a force (Inertia). The second law states that the force exerted by an object is equal to its mass times its acceleration (Force). And the third is that when two moving objects they exert equal and opposite forces on each other (Action and Reaction).
Erwin Schrödinger’s Equation describes how the quantum state of a physical system evolves over time, incorporating the wave-particle duality of matter, which refers to the fact that matter at one moment acts like a wave and yet at another moment acts like matter. This equation has been popularised by the famously related Schrödinger’s Cat thought experiment which was designed to simplify quantum mechanics and which is now referenced in many science fiction works.
If you are interested in studying Maths as a subject, Oxford Open Learning offer you the chance to do so at a variety of levels, listed below. You can also Contact Us here.
To mark British Science Week, from the 8th to the 17th of March, let’s shine a light on some of the greatest contemporary British minds in Science, Technology, Engineering and Maths (or STEM, for short).
Sue Black is a Professor of Computer Science at Durham University. An outspoken and active social media campaigner, Sue led a campaign to save Bletchley Park and is one of the most influential women in tech. An advocate for equality, diversity, and inclusion, particularly for women in computing, she founded BSCWomen, an online network for women in tech, and #techmums, a social enterprise which empowers mothers and their families through technology. In the 2016 New Year Honours, Sue received an OBE for services to technology.
Timothy Berners-Lee is a computer scientist and software engineer who is most famous for inventing Hypertext Transfer Protocol, or HTTP, and the World Wide Web. He also created the first internet browser, the HTML language, and the URL system, and in 1991 was named one of the 100 Most Important People of the 20th Century by Time Magazine. In 2004, Timothy was knighted by Queen Elizabeth II for his pioneering work, and he now works as Professor of Computer Science at the University of Oxford. He is also a professor emeritus at the renowned Massachusetts Institute of Technology (Often referred to as MIT).
Maggie Aderin-Pocock is a space scientist, educator, and communicator. Throughout her career, she has worked on some of the most prestigious projects at some of the UK’s top universities and is currently an honorary research associate within the Department of Physics and Astronomy at University College London and Chancellor at the University of Leicester. She is also a presenter of the TV show The Sky at Night and does much outreach work to engage young people in science. Her academic work now focuses on building instruments and equipment to aid the fight against climate change. Maggie received an MBE for services to science education in 2009 – an honour that was upgraded to OBE in this year’s New Year Honours.
Donald Palmer is an Associate Professor of Immunology at the Royal Veterinary College where his current research interests focus on the ageing of the immune system. After completing his PhD at King’s College London, he took post-doctoral fellowship positions at Cancer Research UK and Imperial College where he carried out research on lymphocyte development. Donald is also a co-founder of the Reach Society – an initiative to inspire, encourage and motivate young people, particularly young Black men and boys, to achieve their full potential.
Roma Agrawal is a structural engineer who is most known for her work on The Shard in London. Born in Mumbai, she completed her undergraduate degree in physics at the University of Oxford and gained an MSc in structural engineering from Imperial College London. She has gained several awards for her work, including the Institute of Structural Engineers’ Structural Engineer of the Year’ award in 2011 and, more recently, the Royal Academy of Engineering’s ‘Rooke Award for Public Promotion of Engineering’. She is an active public speaker and advocate for diversity and inclusion within STEM.
Saiful Islam is Professor of Materials Modelling at the University of Oxford. He gained a chemistry degree and PhD from University College London and his research interests focus on gaining a deeper understanding of the processes that exist within energy materials, particularly batteries. As well as numerous academic awards and honours, Saiful holds a Guinness World Record for the highest voltage lemon battery (usually a low powered, simple battery used for the purposes of education).
To learn about more successful British scientists, visit the Inspiring Scientists website.
If you are interested in studying a Science or Maths, Oxford Open Learning offers the opportunity to do so at a variety of levels, listed below. You can also find advice via our Contact Us page here.
Fast Track Human Biology IGCSE
Perfectionism is not, in and of itself, a negative trait. Perfectionists are often conscientious high achievers; our greatest weakness is also our greatest strength. But those trying to be constantly perfect can find that every task feels like an unconquerable burden and every essay a path to failure, however unlikely our friends and family might find our doom-laden predictions. Here are three thoughts to use to beat the unrealistic idealism that may currently be beating you.
What is perfect, anyway? Maybe you could decide. Perhaps perfection could simply mean sitting down at your messy desk, ignoring the clothes on the floor, and spending 10 minutes planning the first half of your essay. In this deeply imperfect and challenging world, if you were to be reasonable with yourself, your definition of perfect should, and could, be different. Redefine perfection: make it doable and make it your own.
A to-do list is a depressing sight, if, at every item, we are telling ourselves that we ‘have to’ or ‘must’ do this or that. But turn ‘have to’ into ‘get to’ and suddenly life seems more joyful. Perhaps it is an irritating piece of advice, an unwelcome call to simply have more gratitude, but studying is essentially an overwhelmingly positive thing. You are learning and growing, and you have access to great materials and educated teachers; you are lucky. And so, even if it feels at first like you are lying to yourself, tell yourself, next time you inspect your to-do list: “I get to plan my essay today”.
We will do it, but we are waiting for the perfect time when we are in the mood. Because we know we can do it well, and not just well but REALLY well. And so that is the aim. This isn’t laziness, for the fear is real: we cannot bear to submit anything less than our best; we cannot tolerate failure; and we want to be proud of what we have achieved. We have visualised (or we think we have) the perfect essay or assignment. But the truth is that you have a deadline. Perhaps you could achieve perfection if you had eternity to complete it. But you don’t. Most tasks have a timeline, whether it is 6 years to complete a part-time PhD, or one night to finish an essay. And the test is not what you can achieve, but what you can achieve in the time you have to complete it. The definition of perfect might simply be this: finished.
Whatever subject you are studying or qualification you are studying for, contact with your teacher or tutor – even when remote – is an invaluable part of that process. They are usually the subject experts, have a full understanding of the assessment process and have, more often than not, supported many other students who felt exactly the same as you do now about their learning. Whether you are confident in your subject knowledge and looking for ways to stretch yourself in order to achieve the very best results or are still a little uncertain and unsure how you might secure the grade you need, your tutors can provide you with the support you require. Here are a few simple strategies every student should try in order to boost the benefits of the contact they have.
Put simply, meet their expectations! If they provide a task, complete it. If they set a deadline, meet it. If you have a meeting, be there. Programmes of study and assessment schedules are in place to meet the needs of everyone; ensuring that there is adequate time for covering all of the content, assessing progress and providing feedback. A tutor works with many students and if you don’t adhere to the plan then you are unlikely to get the time you deserve. If there is a problem with the schedule set out for you, talk to your tutor in advance so that they can make any amendment they possibly can in order to make sure that everyone’s needs are met. If a tutor sees you are committed to your learning and doing what is required they are likely to go above and beyond in the ways in which they support you.
As already mentioned, the tutor is the subject expert. They have the knowledge of the subject but also the ways it is assessed and how to ensure you can demonstrate it when required to do so. Listen to their advice. Take notes where required. Follow their suggestions. However, if there is something you are unsure about, don’t be afraid to ask! Questioning is key to developing a deeper understanding and mastery of a subject but is also a great tool in ensuring there have been no miscommunications or misunderstandings. Your tutor will respect your ability to really engage with the content you are covering together and look for ways to address your questions in more detail.
Receiving feedback is one of the most important parts of the learning journey. However, many of us find getting feedback something that is really, really hard! Instead of thinking about what is said by your tutor as being ‘good’ or ‘bad’, try to consider what you can learn from it instead. If you are given praise for a certain aspect of your work, think about what you did that made this so effective. If there are comments relating to something that hasn’t worked out so well then think about what you might do differently next time. Reflection is key to making progress. Also, apply the same thought process when it comes to your attitude to learning. If a tutor comments on this, avoid taking it personally and think of how you might use what they have said to become a more effective learner.
Don’t forget that any contact that you have with your tutor is designed to benefit YOU. If you are in need of something specific from that contact then, again, do not be afraid to ask! In reality, this involves planning and preparing for any contact you have before you have it. Make a note of any questions you have when studying independently. If you need to revisit any material with them, ask in advance. If you have found a subject area particularly easy or hard, let them know. Remember, your tutor will be looking to support you in a way that is personalised to meet your needs too, so the more effectively you’re able to communicate these, the better they will be able to do this.
Think of Pythagoras and you’ll probably recall studying his theorem at school, where a right-angled triangle the sum of the squares on the other two shorter sides equals the hypotenuse squared. The theorem is believed to have been known to the Babylonians 1000 years earlier, but the Greek Philosopher and mathematician may have been the first to prove it.
In the field of Mathematics, Pythagoras’ work led to great leaps forward in our understanding of numbers and geometry, and of importance in many other branches of mathematics, including trigonometry.
Pythagoras was taught mathematics by ancient Greek Philosopher Thales, who brought the subject to the Greeks from Ancient Egypt, and by Anaximander, who was an earlier student of Thales. He was founder of the Pythagorean brotherhood, a group devoted to the study of mathematics.
Pythagoras was certainly not an ordinary mathematician, by any means. He believed that science and religion were connected. It is thought that he believed that he had already lived four lives, all of which he could remember. Others claimed that he was able to travel through space and time and could talk to plants and animals.
His work linked his subject with the universe at large. Pythagoreans believed that everything could be reduced to numbers, that the whole universe had been built using mathematics. They said the truth behind the everyday reality we experience lies in numbers.
Modern-day physicists who seek the ‘theory of everything’ or the ‘grand unification’ are Pythagoreans. They subscribe to the thought that the universe can be completely understood through mathematical equations, and they are committed to a quest to find these equations. To Pythagoreans 10 was the supreme number, as it can be made by adding the first four numbers, 1,2,3 and 4. These numbers form a tetractys – the perfect, equilateral triangle.
Pythagoreans also used science in the areas of mystery and spiritualism. Their beliefs were based on the power of numbers. The monad (a unit), spoke of the birthplace of all things, and the number two, the dyad, referred to matter. The number seven was considered sacred because it was the number of strings on a lyre, the number of planets, and the seventh day of the Greek calendar was sacred to Apollo, all the feasts were celebrated on the seventh of the month.
Pythagoras also recognised the healing powers of music. He thought it was possible to align the souls to their perfect nature, and through music he performed what he called ‘soul adjustments’. He was the first person to prescribe music as medicine.
Widely considered as the ‘father of philosophy’, Pythagoras’ teachings, theories, philosophies and life’s work show that he was truly an outstanding polymath, and his learnings and teachings made him one of the greatest thinkers of his time.