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Home/Chain Registry/Block #2,187,865

Block #2,187,865

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/1/2017, 11:22:41 AM Β· Difficulty 10.9477 Β· 4,651,032 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8ee4e326147d2609cfaad1b69d451b9b688d9299271b837043339ab5c44c698c
View on Chainz β†—

Difficulty

10.947663

Transactions

1

Size

201 B

Version

2

Bits

0af29a07

Nonce

151,092,551

Timestamp

7/1/2017, 11:22:41 AM

Confirmations

4,651,032

Merkle Root

4ec4dbbbda88abced9842cbea4d8f0fb8b7fe8712281b692fa9b58d5606852c8
Transactions (1)
Coinbase4ec4dbbbda88ab…9b58d5606852c8
1 in β†’ 1 out8.3300 XPM110 B
AKjtn8v8…gcckN6pP
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.

1.105 Γ— 10⁹⁢(97-digit number)
11056309174876133430…53382606622432650240
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
1.105 Γ— 10⁹⁢(97-digit number)
11056309174876133430…53382606622432650239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.105 Γ— 10⁹⁢(97-digit number)
11056309174876133430…53382606622432650241
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
2.211 Γ— 10⁹⁢(97-digit number)
22112618349752266861…06765213244865300479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.211 Γ— 10⁹⁢(97-digit number)
22112618349752266861…06765213244865300481
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
4.422 Γ— 10⁹⁢(97-digit number)
44225236699504533722…13530426489730600959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.422 Γ— 10⁹⁢(97-digit number)
44225236699504533722…13530426489730600961
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
8.845 Γ— 10⁹⁢(97-digit number)
88450473399009067445…27060852979461201919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.845 Γ— 10⁹⁢(97-digit number)
88450473399009067445…27060852979461201921
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
1.769 Γ— 10⁹⁷(98-digit number)
17690094679801813489…54121705958922403839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.769 Γ— 10⁹⁷(98-digit number)
17690094679801813489…54121705958922403841
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
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 2187865

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 8ee4e326147d2609cfaad1b69d451b9b688d9299271b837043339ab5c44c698c

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 #2,187,865 on Chainz β†—
Circulating Supply:57,955,443 XPMΒ·at block #6,838,896 Β· updates every 60s
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