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Block #840,549

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/5/2014, 5:58:13 AM Β· Difficulty 10.9742 Β· 6,001,290 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ed271e9d7d38f07109d2dbffcf4f1221b468a1b1e4d4b3acfe869caa129ada91
View on Chainz β†—

Height

#840,549

Difficulty

10.974200

Transactions

2

Size

722 B

Version

2

Bits

0af96527

Nonce

1,783,553,451

Timestamp

12/5/2014, 5:58:13 AM

Confirmations

6,001,290

Mined by

⛏️ P2SHAM7Su1iKLefgh9Fkq62jroqRUsLYXq2ErT

Merkle Root

7e9faa8792b8b4805c5089522de6ddb9928273ca17e174173fcc356e2e0a5cd8
Transactions (2)
Coinbase931639e5c29a37…956cf78b58d3d5
1 in β†’ 1 out8.3050 XPM110 B
AM7Su1iK…LYXq2ErT
5dbe3a2f66d855…b50718a63e3aad
3 in β†’ 2 out0.0217 XPM523 B
ASPuJKq7…H6fYLFrLAN8FvDpM…1AxfzaKi
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.

5.221 Γ— 10⁹¹(92-digit number)
52214782934488691616…62698210416669825919
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
5.221 Γ— 10⁹¹(92-digit number)
52214782934488691616…62698210416669825919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.221 Γ— 10⁹¹(92-digit number)
52214782934488691616…62698210416669825921
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
1.044 Γ— 10⁹²(93-digit number)
10442956586897738323…25396420833339651839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.044 Γ— 10⁹²(93-digit number)
10442956586897738323…25396420833339651841
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
2.088 Γ— 10⁹²(93-digit number)
20885913173795476646…50792841666679303679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.088 Γ— 10⁹²(93-digit number)
20885913173795476646…50792841666679303681
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
4.177 Γ— 10⁹²(93-digit number)
41771826347590953293…01585683333358607359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.177 Γ— 10⁹²(93-digit number)
41771826347590953293…01585683333358607361
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
8.354 Γ— 10⁹²(93-digit number)
83543652695181906586…03171366666717214719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.354 Γ— 10⁹²(93-digit number)
83543652695181906586…03171366666717214721
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:57,979,086 XPMΒ·at block #6,841,838 Β· updates every 60s
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