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Home/Chain Registry/Block #2,684,251

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· 4,152,094 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†—

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

4,152,094

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…80257330363832939520
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12
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
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2684251

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock bf7c8320966173fb337a4be4b559fa98b4f22d80c4e3c6c36f2ec88fcc14cf67

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,684,251 on Chainz β†—
Circulating Supply:57,935,018 XPMΒ·at block #6,836,344 Β· updates every 60s
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