XPM Prime Explorer symbol
XPMPrime Explorer

Block #545,992

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/15/2014, 3:50:46 PM Β· Difficulty 10.9549 Β· 6,264,193 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
6c0f79c911ffed089861b5c56bcb44f05888f60905d475254c0cc4487dc6d631
View on Chainz β†—

Height

#545,992

Difficulty

10.954879

Transactions

1

Size

243 B

Version

2

Bits

0af472ec

Nonce

182,836,534

Timestamp

5/15/2014, 3:50:46 PM

Confirmations

6,264,193

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

200bc036a734120c0d37a316610cf1ef21b32060bc333002e94785529c5049cc
Transactions (1)
Coinbase200bc036a73412…4785529c5049cc
1 in β†’ 2 out8.3200 XPM152 B
ARzmpY4c…fvx8bF9tALPu3s2c…EJXLjVFh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.077 Γ— 10⁹⁸(99-digit number)
10773196936203736905…39661340328575947679
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.077 Γ— 10⁹⁸(99-digit number)
10773196936203736905…39661340328575947679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.077 Γ— 10⁹⁸(99-digit number)
10773196936203736905…39661340328575947681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.154 Γ— 10⁹⁸(99-digit number)
21546393872407473811…79322680657151895359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.154 Γ— 10⁹⁸(99-digit number)
21546393872407473811…79322680657151895361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.309 Γ— 10⁹⁸(99-digit number)
43092787744814947622…58645361314303790719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.309 Γ— 10⁹⁸(99-digit number)
43092787744814947622…58645361314303790721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
8.618 Γ— 10⁹⁸(99-digit number)
86185575489629895244…17290722628607581439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.618 Γ— 10⁹⁸(99-digit number)
86185575489629895244…17290722628607581441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.723 Γ— 10⁹⁹(100-digit number)
17237115097925979048…34581445257215162879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.723 Γ— 10⁹⁹(100-digit number)
17237115097925979048…34581445257215162881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.447 Γ— 10⁹⁹(100-digit number)
34474230195851958097…69162890514430325759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,725,549 XPMΒ·at block #6,810,184 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy