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Home/Chain Registry/Block #2,129,991

Block #2,129,991

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2017, 3:14:17 AM Β· Difficulty 10.9094 Β· 4,712,533 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8f4462aca09c5ff7e51e9a664c43442a52253dccb56a83b7e5f325ea4152617a
View on Chainz β†—

Difficulty

10.909401

Transactions

1

Size

200 B

Version

2

Bits

0ae8ce80

Nonce

1,718,360,657

Timestamp

5/24/2017, 3:14:17 AM

Confirmations

4,712,533

Merkle Root

492ae1b77ad038ff2d2c341631547c3522edd7d4390f84658b3d493b5e755ac7
Transactions (1)
Coinbase492ae1b77ad038…3d493b5e755ac7
1 in β†’ 1 out8.3900 XPM110 B
AV7HSRca…h8D2dXn2
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.

8.444 Γ— 10⁹⁡(96-digit number)
84443733927815268010…55541120211054535680
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
8.444 Γ— 10⁹⁡(96-digit number)
84443733927815268010…55541120211054535679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.444 Γ— 10⁹⁡(96-digit number)
84443733927815268010…55541120211054535681
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
1.688 Γ— 10⁹⁢(97-digit number)
16888746785563053602…11082240422109071359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.688 Γ— 10⁹⁢(97-digit number)
16888746785563053602…11082240422109071361
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
3.377 Γ— 10⁹⁢(97-digit number)
33777493571126107204…22164480844218142719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.377 Γ— 10⁹⁢(97-digit number)
33777493571126107204…22164480844218142721
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
6.755 Γ— 10⁹⁢(97-digit number)
67554987142252214408…44328961688436285439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.755 Γ— 10⁹⁢(97-digit number)
67554987142252214408…44328961688436285441
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
1.351 Γ— 10⁹⁷(98-digit number)
13510997428450442881…88657923376872570879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.351 Γ— 10⁹⁷(98-digit number)
13510997428450442881…88657923376872570881
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 2129991

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 8f4462aca09c5ff7e51e9a664c43442a52253dccb56a83b7e5f325ea4152617a

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 #2,129,991 on Chainz β†—
Circulating Supply:57,984,613 XPMΒ·at block #6,842,523 Β· updates every 60s
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