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Block #1,812,789

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/18/2016, 6:03:53 PM Β· Difficulty 10.7789 Β· 5,014,077 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5d993fe456f5a37a32c841884b43c6565c9bcd3f96b3d6da0ba07d42a43f8be4
View on Chainz β†—

Height

#1,812,789

Difficulty

10.778944

Transactions

2

Size

459 B

Version

2

Bits

0ac768dd

Nonce

1,975,356,073

Timestamp

10/18/2016, 6:03:53 PM

Confirmations

5,014,077

Mined by

⛏️ P2SHAN3ZJjkqdXfdAcpNPiZczLhanj7xTmR3dE

Merkle Root

69a5d688942b4752835f3c5d0ca6454e2bbb1b9be84851c6420171757da78b5f
Transactions (2)
Coinbasef3a9ab10049e59…e13513d94481c5
1 in β†’ 1 out8.6000 XPM110 B
AN3ZJjkq…7xTmR3dE
54804ab2493b35…09f653933cc40b
1 in β†’ 3 out25.0297 XPM259 B
AYVhtVtw…cH5tp8HuAR6qgsuL…x1tjMz93AKsebF9o…26T4a6vn
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.

2.288 Γ— 10⁹⁡(96-digit number)
22881414440290054428…64096552210111053919
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
2.288 Γ— 10⁹⁡(96-digit number)
22881414440290054428…64096552210111053919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.288 Γ— 10⁹⁡(96-digit number)
22881414440290054428…64096552210111053921
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
4.576 Γ— 10⁹⁡(96-digit number)
45762828880580108856…28193104420222107839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.576 Γ— 10⁹⁡(96-digit number)
45762828880580108856…28193104420222107841
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
9.152 Γ— 10⁹⁡(96-digit number)
91525657761160217712…56386208840444215679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.152 Γ— 10⁹⁡(96-digit number)
91525657761160217712…56386208840444215681
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
1.830 Γ— 10⁹⁢(97-digit number)
18305131552232043542…12772417680888431359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.830 Γ— 10⁹⁢(97-digit number)
18305131552232043542…12772417680888431361
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
3.661 Γ— 10⁹⁢(97-digit number)
36610263104464087085…25544835361776862719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.661 Γ— 10⁹⁢(97-digit number)
36610263104464087085…25544835361776862721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,859,090 XPMΒ·at block #6,826,865 Β· updates every 60s
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