XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,684,251

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 9:19:37 AM Β· Difficulty 11.6909 Β· 4,152,742 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf7c8320966173fb337a4be4b559fa98b4f22d80c4e3c6c36f2ec88fcc14cf67
View on Chainz β†—

Height

#2,684,251

Difficulty

11.690923

Transactions

1

Size

198 B

Version

2

Bits

0bb0e057

Nonce

1,375,046,396

Timestamp

5/30/2018, 9:19:37 AM

Confirmations

4,152,742

Mined by

⛏️ P2SHAVJP7CXMB1VTsCYZRbaNej7VPVGBki8aCL

Merkle Root

1645d43f675a8f06fb1657fdd5842f09cdcd81f547498e2f373b139555891d37
Transactions (1)
Coinbase1645d43f675a8f…3b139555891d37
1 in β†’ 1 out7.3000 XPM109 B
AVJP7CXM…GBki8aCL
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.

2.868 Γ— 10⁹³(94-digit number)
28686431019616080111…80257330363832939519
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
2.868 Γ— 10⁹³(94-digit number)
28686431019616080111…80257330363832939519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.868 Γ— 10⁹³(94-digit number)
28686431019616080111…80257330363832939521
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
5.737 Γ— 10⁹³(94-digit number)
57372862039232160223…60514660727665879039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.737 Γ— 10⁹³(94-digit number)
57372862039232160223…60514660727665879041
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
1.147 Γ— 10⁹⁴(95-digit number)
11474572407846432044…21029321455331758079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.147 Γ— 10⁹⁴(95-digit number)
11474572407846432044…21029321455331758081
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
2.294 Γ— 10⁹⁴(95-digit number)
22949144815692864089…42058642910663516159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.294 Γ— 10⁹⁴(95-digit number)
22949144815692864089…42058642910663516161
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
4.589 Γ— 10⁹⁴(95-digit number)
45898289631385728179…84117285821327032319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.589 Γ— 10⁹⁴(95-digit number)
45898289631385728179…84117285821327032321
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
9.179 Γ— 10⁹⁴(95-digit number)
91796579262771456358…68234571642654064639
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
9.179 Γ— 10⁹⁴(95-digit number)
91796579262771456358…68234571642654064641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,940,245 XPMΒ·at block #6,836,992 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.
Privacy PolicyΒ·
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