Latest news with #Euler
Yahoo
2 days ago
- Business
- Yahoo
DeFi Sector TVL Hits 3-Year High of $153B as Investors Rush to Farm Yields
The decentralized finance (DeFi) market ballooned to a three-year high of $153 billion on Monday, spurred by ETH's ascent toward $4,000 and significant inflows into restaking protocols. DefiLlama data shows that the uptick in inflows and asset prices over the past week lifted the sector above its December 2024 high to its highest point since May 2022, at the time of $60 billion collapse of Do Kwon's Terra network. ETH has risen 60% from $2,423 to $3,887 over the past 30 days following a wave of institutional investment including a $1.3 billion treasury investment from Sharplink Gaming and BitMine's $2 billion acquisition. Ethereum still commands the monopoly over DeFi total value locked (TVL) with 59.5% of all capital locked on-chain, the majority of which can be attributed to liquid staking protocol Lido and lending platform Aave, both of which have between $32 billion and $34 billion in TVL. Institutions acquiring assets like ether is one part of the equation, the other is securing a yield on top of that investment. Investors can stake ETH directly and earn a modest annual yield between 1.5% and 4%, or they can go one step further and use a restaking protocol, which will award native yield and a liquid staking token that can be used elsewhere across the DeFi ecosystem for additional yield. X user OlimpioCrypto revealed a more complex strategy that can secure an annual return of up to 25% on USDC and sUSDC with low risk and full liquidity. It loops assets between Euler and Spark on Unichain: Users supply USDC on Euler, borrow sUSDC, re-supply it, and repeat. Incentives from Spark (SSR + OP rewards) and Euler (USDC subsidies, rEUL) boost returns. An easier but less profitable alternative starts by minting sUSDC via Spark and looping with USDC borrow/lend on Euler. Despite UI discrepancies, both methods are reportedly yielding strong returns, likely lasting about a week unless incentives change. While much of the attention is understandably on the Ethereum network, Solana's TVL has grown by 23% in the past month to $12 billion, with protocols like Sanctum, Jupiter and Marinade all outperforming the wider SOL ecosystem with significant inflows, according to DefiLlama. Investors have also been pouring capital into Avalanche and Sui, which are up 33% and 39%, respectively, in terms of TVL this month. The Bitcoin DeFi ecosystem has been more muted, rising by just 9% to $6.2 billion despite a recent drive to new record highs at $124,000.
Yahoo
3 days ago
- Business
- Yahoo
Euler DAO votes to boost revenue 414% with new fees amid red-hot lending competition
Euler DAO, the crypto collective behind the popular lending protocol, is voting on a proposal to selectively increase fees on its products, potentially boosting revenue by 414%. If passed, the proposal will add a 10% fee on Euler Prime stablecoin vaults and a 10% fee on all Euler Yield vaults. Fees on all other products will remain the same. 'The selective strategy is smarter because the fee rate can be adjusted to suit the unique profiles of lenders and borrowers in each vault,' Anton Totomanov, founder of Objective Labs, told DL News. Objective Labs, a risk management partner of Euler Labs, devised the proposal's fee recommendations. According to Objective Labs' calculations, the new fees will increase the DAO's annual revenue from $714,000 to over $3.6 million, giving the crypto collective a bigger pool of funds to play with. However, the new fees will cut into the profit that Euler users can earn on their crypto. Some could look elsewhere for better places to deposit their assets. Euler is a DeFi lending protocol similar to Aave. It is made up of dozens of vaults where users can borrow crypto against various forms of collateral, such as other crypto assets or even DeFi protocol deposits. In 2023, the protocol was hit by a $200 million hack. Although the attacker later returned the funds, the incident shook investor confidence in Euler, and the protocol remained dormant for over a year before relaunching in September. Increased competition In recent months, competition among DeFi lenders has intensified as the market reaches an all-time high of $112 billion. Earlier this month, Aave's DAO voted to launch a white-label lending protocol on Kraken's Ink blockchain in a bid to tap into the centralised exchange's customer base. In January, Morpho did something similar when it signed a deal with Coinbase to facilitate Bitcoin-backed loans for the exchange's customers. Other DeFi lenders, such as Maple and Sky, are also locked in battle over institutional customers. Euler adding more fees at such a critical time could be risky. The protocol held off doing so initially to be as attractive and competitive as possible when it relaunched. But now the protocol has grown to almost $2.5 billion in deposits, it could add fees without having a negative impact, Seini, the proposal's pseudonymous author said. Balancing act Totomanov said that introducing fees to the Euler Yield vaults is unlikely to have a negative impact because they are already designed to offer higher yields to investors by taking on more risk. However, for other vaults, such as those facilitating the lending and borrowing of Ethereum, adding a fee could be more detrimental. That's because 90% of Ethereum borrowers on Euler are engaged in looping, a strategy where lenders juice their Ethereum staking yields by repeatedly depositing and borrowing Ethereum. These users are particularly sensitive to changes in borrowing rates. Last week, the sudden withdrawal of $1.7 billion in Ethereum from Aave caused Ethereum borrowing rates to spike, triggering a scramble to unwind looping trades. 'Charging high fees on ETH inside Euler Prime would lead to a modest revenue increase while possibly leading to outflows,' Totomanov said, explaining why Objective Labs decided not to implement a fee on Euler Prime's Ethereum market. So far, 100% of voters support enabling fees in accordance with Objective Labs' recommendations, or going further and giving the firm full control over fee management. The vote is set to end on Wednesday. Tim Craig is DL News' Edinburgh-based DeFi Correspondent. Reach out with tips at tim@ Error in retrieving data Sign in to access your portfolio Error in retrieving data Error in retrieving data Error in retrieving data Error in retrieving data
Hindustan Times
02-06-2025
- Science
- Hindustan Times
Chicken and egg — and duck too
Here at Problematics we usually aim for puzzles that are not the kind you would find in a textbook, but there are exceptions. Some puzzles that can be solved with textbook methods are still interesting because of the way they are packaged or because of their pedigree, with illustrious minds having dwelt on them at some point in history. A prime example of puzzles that are delightful because of both packaging and pedigree are the problems in Bhaskara's Lilavati. While those are widely known, I recently found one that I hadn't come across earlier. It is said to have appeared in a book by the great Euler, and described by the French writer Stendhal before making its way into the writings of the late Russian mathematician Yakov Perelman. To insulate the solution from an internet search, I have added my customary modifications to the version described by Perelman. I have changed the currency to Indian rupees, and tinkered with the prices to bring them within a range that is credible for the story into which I have packaged my adaptation. The story, of course, is entirely my own. #Puzzle 145.1 A family of poultry farmers collects 100 eggs one morning. They are all chicken and duck eggs, the distribution being unequal. Handing the chicken eggs to their son and the duck eggs to their daughter, the farmer parents send them off to the market. The price for each kind is fixed, with the duck eggs being costlier than chicken eggs, as is the case in most places. Each child sells his or her full share of eggs at the respective fixed rates. In the evening, when they compare their earnings, they are thrilled to find that both have made exactly the same amount. I am no farmer, but the internet tells me that hens and ducks lay about one egg daily at the peak of their productive years. It is not surprising, therefore, that the same birds at our farm lay the same number of eggs the following morning. In other words, the family has 100 eggs again, and the unequal distribution of chicken and duck eggs is the same as on the previous day. Mother segregates the produce into a number of baskets, the chicken eggs on one side, the duck eggs on another. Father passes the orders: 'Pick up your respective shares and come back with the same earnings as you did yesterday.' The kids get mixed up, of course (how else would there be a puzzle?) The son picks up the duck eggs by mistake, and the daughter takes the rest. Neither of them notices that his or her count is not the same as on the previous day. At the market, the boy sells the duck eggs at the price for chicken eggs, and his sister sells the chicken eggs at the price for duck eggs. When they compare their earnings in the evening, the boy is alarmed. 'I got only ₹280 today. I don't know how I can explain this to Father,' he says. The girl is equally puzzled about her collection, but pleasantly so. 'I don't know how, but my earnings rose to ₹630 today,' she tells her brother. #Puzzle 145.2 MAILBOX: LAST WEEK'S SOLVERS Hi Kabir, Assuming that the store owner initially bought cat food for 31 cats for N days, or 31N cans. As each cat consumes 1 can/day, the total consumption reduces by 1 can every day. Again, all cans were consumed in one day less than twice the number of days originally planned, or (2N – 1) days. Thus the total number of cans is the sum of an arithmetic progression of (2N – 1) terms starting 31, and with a common difference of –1. The sum of the AP is: [(2N – 1)/2][2*31 + (2N – 1 – 1) (–1)] = 65N – 32 – 2N² Equating the above to 31N and simplifying, we get the equation 2N² – 34N + 32 = 0. The roots of this equation are N = 16 and 1. As 1 day is not viable, N must be 16. So the total number of cans bought initially = 31*16 = 496. And as it took (2N –1) = 31 days to finish the whole stock of food, only 1 cat was left unsold. — Anil Khanna, Ghaziabad *** Hi Kabir, Suppose the cat food was initially ordered for N days. Then, the number of cans ordered = 31N. Also, suppose K is the number of cats remaining unsold when the food stock got exhausted. On any day, the number of cans consumed is the equal to total number of unsold cats. Thus the total cans consumed = 31 + 30 + 29… + (K + 2) + (K + 1) + K = (31 + K)(31 – K + 1)/2 i.e. 31N = (31 + K)(31 – K + 1)/2 For the right-hand side to be a multiple of 31, K has to be 1. This means 31N = 32*31/2, or N = 16. The number of cans = 31 x 16 = 496. The food lasted for 31 days. If we add one more day, we get 32 days which is twice the original period of 16 days. — Professor Anshul Kumar, Delhi From Professor Kumar's approach, it emerges that the puzzle can be solved even without the information about the cans being exhausted in (2N – 1) days. Many readers, however, have used this bit in solving the puzzle. Puzzle #144.2 Hi Kabir, The puzzle about the party trick is fairly simple — you randomly tap on any two animal names for the first and second taps and then tap in the order of length of the animal names — i.e. COW (third tap), LION, HORSE, MONKEY, OSTRICH, ELEPHANT, BUTTERFLY AND RHINOCEROS. Obviously, this trick will get old very soon because your tapping pattern will become predictable to a keen observer. — Abhinav Mital, Singapore Solved both puzzles: Anil Khanna (Ghaziabad), Professor Anshul Kumar (Delhi), Abhinav Mital (Singapore), Kanwarjit Singh (Chief Commissioner of Income-tax, retd), Dr Sunita Gupta (Delhi), Yadvendra Somra (Sonipat), Shishir Gupta (Indore), Ajay Ashok (Delhi), YK Munjal (Delhi), Sampath Kumar V (Coimbatore) Solved #Puzzle 144.1: Vinod Mahajan (Delhi)
Gizmodo
31-05-2025
- General
- Gizmodo
A Brief History of Our Obsession With Prime Numbers—and Where the Hunt Goes Next
A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes a number system built on prime numbers. As the Ishango bone, the Plimpton 322 tablet and other artifacts throughout history display, prime numbers have fascinated and captivated people throughout history. Today, prime numbers and their properties are studied in number theory, a branch of mathematics and active area of research today. A history of prime numbers Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number since 11 dots form only rectangular arrays of sizes 1 by 11 and 11 by 1. Conversely, 12 is not prime since you can use 12 dots to make an array of 3 by 4 dots, with multiple rows and multiple columns. Math textbooks define a prime number as a whole number greater than one whose only positive divisors are only 1 and itself. Math historian Peter S. Rudman suggests that Greek mathematicians were likely the first to understand the concept of prime numbers, around 500 B.C.E. Around 300 B.C.E., the Greek mathematician and logician Euler proved that there are infinitely many prime numbers. Euler began by assuming that there is a finite number of primes. Then he came up with a prime that was not on the original list to create a contradiction. Since a fundamental principle of mathematics is being logically consistent with no contradictions, Euler then concluded that his original assumption must be false. So, there are infinitely many primes. The argument established the existence of infinitely many primes, however it was not particularly constructive. Euler had no efficient method to list all the primes in an ascending list. In the middle ages, Arab mathematicians advanced the Greeks' theory of prime numbers, referred to as hasam numbers during this time. The Persian mathematician Kamal al-Din al-Farisi formulated the fundamental theorem of arithmetic, which states that any positive integer larger than one can be expressed uniquely as a product of primes. From this view, prime numbers are the basic building blocks for constructing any positive whole number using multiplication – akin to atoms combining to make molecules in chemistry. Prime numbers can be sorted into different types. In 1202, Leonardo Fibonacci introduced in his book 'Liber Abaci: Book of Calculation' prime numbers of the form (2p – 1) where p is also prime. Today, primes in this form are called Mersenne primes after the French monk Marin Mersenne. Many of the largest known primes follow this format. Several early mathematicians believed that a number of the form (2p – 1) is prime whenever p is prime. But in 1536, mathematician Hudalricus Regius noticed that 11 is prime but not (211 – 1), which equals 2047. The number 2047 can be expressed as 11 times 89, disproving the conjecture. While not always true, number theorists realized that the (2p – 1) shortcut often produces primes and gives a systematic way to search for large primes. The search for large primes The number (2p – 1) is much larger relative to the value of p and provides opportunities to identify large primes. When the number (2p – 1) becomes sufficiently large, it is much harder to check whether (2p – 1) is prime – that is, if (2p – 1) dots can be arranged only into a rectangular array with one column or one row. Fortunately, Édouard Lucas developed a prime number test in 1878, later proved by Derrick Henry Lehmer in 1930. Their work resulted in an efficient algorithm for evaluating potential Mersenne primes. Using this algorithm with hand computations on paper, Lucas showed in 1876 that the 39-digit number (2127 – 1) equals 170,141,183,460,469,231,731,687,303,715,884,105,727, and that value is prime. Also known as M127, this number remains the largest prime verified by hand computations. It held the record for largest known prime for 75 years. Researchers began using computers in the 1950s, and the pace of discovering new large primes increased. In 1952, Raphael M. Robinson identified five new Mersenne primes using a Standard Western Automatic Computer to carry out the Lucas-Lehmer prime number tests. As computers improved, the list of Mersenne primes grew, especially with the Cray supercomputer's arrival in 1964. Although there are infinitely many primes, researchers are unsure how many fit the type (2p – 1) and are Mersenne primes. By the early 1980s, researchers had accumulated enough data to confidently believe that infinitely many Mersenne primes exist. They could even guess how often these prime numbers appear, on average. Mathematicians have not found proof so far, but new data continues to support these guesses. George Woltman, a computer scientist, founded the Great Internet Mersenne Prime Search, or GIMPS, in 1996. Through this collaborative program, anyone can download freely available software from the GIMPS website to search for Mersenne prime numbers on their personal computers. The website contains specific instructions on how to participate. GIMPS has now identified 18 Mersenne primes, primarily on personal computers using Intel chips. The program averages a new discovery about every one to two years. The largest known prime Luke Durant, a retired programmer, discovered the current record for the largest known prime, (2136,279,841 – 1), in October 2024. Referred to as M136279841, this 41,024,320-digit number was the 52nd Mersenne prime identified and was found by running GIMPS on a publicly available cloud-based computing network. This network used Nvidia chips and ran across 17 countries and 24 data centers. These advanced chips provide faster computing by handling thousands of calculations simultaneously. The result is shorter run times for algorithms such as prime number testing. The Electronic Frontier Foundation is a civil liberty group that offers cash prizes for identifying large primes. It awarded prizes in 2000 and 2009 for the first verified 1 million-digit and 10 million-digit prime numbers. Large prime number enthusiasts' next two challenges are to identify the first 100 million-digit and 1 billion-digit primes. EFF prizes of US$150,000 and $250,000, respectively, await the first successful individual or group. Eight of the 10 largest known prime numbers are Mersenne primes, so GIMPS and cloud computing are poised to play a prominent role in the search for record-breaking large prime numbers. Large prime numbers have a vital role in many encryption methods in cybersecurity, so every internet user stands to benefit from the search for large prime numbers. These searches help keep digital communications and sensitive information safe. Jeremiah Bartz, Associate Professor of Mathematics, University of North Dakota. This article is republished from The Conversation under a Creative Commons license. Read the original article.
Yahoo
30-05-2025
- Science
- Yahoo
Prime numbers, the building blocks of mathematics, have fascinated for centuries − now technology is revolutionizing the search for them
A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes a number system built on prime numbers. As the Ishango bone, the Plimpton 322 tablet and other artifacts throughout history display, prime numbers have fascinated and captivated people throughout history. Today, prime numbers and their properties are studied in number theory, a branch of mathematics and active area of research today. Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number since 11 dots form only rectangular arrays of sizes 1 by 11 and 11 by 1. Conversely, 12 is not prime since you can use 12 dots to make an array of 3 by 4 dots, with multiple rows and multiple columns. Math textbooks define a prime number as a whole number greater than one whose only positive divisors are only 1 and itself. Math historian Peter S. Rudman suggests that Greek mathematicians were likely the first to understand the concept of prime numbers, around 500 B.C.E. Around 300 B.C.E., the Greek mathematician and logician Euler proved that there are infinitely many prime numbers. Euler began by assuming that there is a finite number of primes. Then he came up with a prime that was not on the original list to create a contradiction. Since a fundamental principle of mathematics is being logically consistent with no contradictions, Euler then concluded that his original assumption must be false. So, there are infinitely many primes. The argument established the existence of infinitely many primes, however it was not particularly constructive. Euler had no efficient method to list all the primes in an ascending list. In the middle ages, Arab mathematicians advanced the Greeks' theory of prime numbers, referred to as hasam numbers during this time. The Persian mathematician Kamal al-Din al-Farisi formulated the fundamental theorem of arithmetic, which states that any positive integer larger than one can be expressed uniquely as a product of primes. From this view, prime numbers are the basic building blocks for constructing any positive whole number using multiplication – akin to atoms combining to make molecules in chemistry. Prime numbers can be sorted into different types. In 1202, Leonardo Fibonacci introduced in his book 'Liber Abaci: Book of Calculation' prime numbers of the form (2p - 1) where p is also prime. Today, primes in this form are called Mersenne primes after the French monk Marin Mersenne. Many of the largest known primes follow this format. Several early mathematicians believed that a number of the form (2p – 1) is prime whenever p is prime. But in 1536, mathematician Hudalricus Regius noticed that 11 is prime but not (211 - 1), which equals 2047. The number 2047 can be expressed as 11 times 89, disproving the conjecture. While not always true, number theorists realized that the (2p - 1) shortcut often produces primes and gives a systematic way to search for large primes. The number (2p – 1) is much larger relative to the value of p and provides opportunities to identify large primes. When the number (2p - 1) becomes sufficiently large, it is much harder to check whether (2p - 1) is prime – that is, if (2p - 1) dots can be arranged only into a rectangular array with one column or one row. Fortunately, Édouard Lucas developed a prime number test in 1878, later proved by Derrick Henry Lehmer in 1930. Their work resulted in an efficient algorithm for evaluating potential Mersenne primes. Using this algorithm with hand computations on paper, Lucas showed in 1876 that the 39-digit number (2127 - 1) equals 170,141,183,460,469,231,731,687,303,715,884,105,727, and that value is prime. Also known as M127, this number remains the largest prime verified by hand computations. It held the record for largest known prime for 75 years. Researchers began using computers in the 1950s, and the pace of discovering new large primes increased. In 1952, Raphael M. Robinson identified five new Mersenne primes using a Standard Western Automatic Computer to carry out the Lucas-Lehmer prime number tests. As computers improved, the list of Mersenne primes grew, especially with the Cray supercomputer's arrival in 1964. Although there are infinitely many primes, researchers are unsure how many fit the type (2p - 1) and are Mersenne primes. By the early 1980s, researchers had accumulated enough data to confidently believe that infinitely many Mersenne primes exist. They could even guess how often these prime numbers appear, on average. Mathematicians have not found proof so far, but new data continues to support these guesses. George Woltman, a computer scientist, founded the Great Internet Mersenne Prime Search, or GIMPS, in 1996. Through this collaborative program, anyone can download freely available software from the GIMPS website to search for Mersenne prime numbers on their personal computers. The website contains specific instructions on how to participate. GIMPS has now identified 18 Mersenne primes, primarily on personal computers using Intel chips. The program averages a new discovery about every one to two years. Luke Durant, a retired programmer, discovered the current record for the largest known prime, (2136,279,841 - 1), in October 2024. Referred to as M136279841, this 41,024,320-digit number was the 52nd Mersenne prime identified and was found by running GIMPS on a publicly available cloud-based computing network. This network used Nvidia chips and ran across 17 countries and 24 data centers. These advanced chips provide faster computing by handling thousands of calculations simultaneously. The result is shorter run times for algorithms such as prime number testing. The Electronic Frontier Foundation is a civil liberty group that offers cash prizes for identifying large primes. It awarded prizes in 2000 and 2009 for the first verified 1 million-digit and 10 million-digit prime numbers. Large prime number enthusiasts' next two challenges are to identify the first 100 million-digit and 1 billion-digit primes. EFF prizes of US$150,000 and $250,000, respectively, await the first successful individual or group. Eight of the 10 largest known prime numbers are Mersenne primes, so GIMPS and cloud computing are poised to play a prominent role in the search for record-breaking large prime numbers. Large prime numbers have a vital role in many encryption methods in cybersecurity, so every internet user stands to benefit from the search for large prime numbers. These searches help keep digital communications and sensitive information safe. This article is republished from The Conversation, a nonprofit, independent news organization bringing you facts and trustworthy analysis to help you make sense of our complex world. It was written by: Jeremiah Bartz, University of North Dakota Read more: Planning the best route with multiple destinations is hard even for supercomputers – a new approach breaks a barrier that's stood for nearly half a century Why does nature create patterns? A physicist explains the molecular-level processes behind crystals, stripes and basalt columns Art and science illuminate the same subtle proportions in tree branches Jeremiah Bartz owns shares in Nvidia.
