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Home/Chain Registry/Block #2,129,239

Block #2,129,239

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/23/2017, 1:44:11 PM Β· Difficulty 10.9104 Β· 4,708,905 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ab932a17c0212967ef7a8849f8d1bc1e24f9bbc67ac1a773dc9db364e85fde4
View on Chainz β†—

Difficulty

10.910394

Transactions

1

Size

199 B

Version

2

Bits

0ae90f9d

Nonce

493,786,876

Timestamp

5/23/2017, 1:44:11 PM

Confirmations

4,708,905

Merkle Root

977f09647339dbc5a4b8d0f5c6db8e9eb8aa687aa677bdc0b74eb3a83b777f59
Transactions (1)
Coinbase977f09647339db…4eb3a83b777f59
1 in β†’ 1 out8.3900 XPM109 B
AZx8PYcd…p55skwHK
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.

1.434 Γ— 10⁹⁡(96-digit number)
14344465821026316419…06540594036631676160
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
1.434 Γ— 10⁹⁡(96-digit number)
14344465821026316419…06540594036631676159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.434 Γ— 10⁹⁡(96-digit number)
14344465821026316419…06540594036631676161
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
2.868 Γ— 10⁹⁡(96-digit number)
28688931642052632838…13081188073263352319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.868 Γ— 10⁹⁡(96-digit number)
28688931642052632838…13081188073263352321
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
5.737 Γ— 10⁹⁡(96-digit number)
57377863284105265677…26162376146526704639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.737 Γ— 10⁹⁡(96-digit number)
57377863284105265677…26162376146526704641
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
1.147 Γ— 10⁹⁢(97-digit number)
11475572656821053135…52324752293053409279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.147 Γ— 10⁹⁢(97-digit number)
11475572656821053135…52324752293053409281
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
2.295 Γ— 10⁹⁢(97-digit number)
22951145313642106270…04649504586106818559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.295 Γ— 10⁹⁢(97-digit number)
22951145313642106270…04649504586106818561
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
4.590 Γ— 10⁹⁢(97-digit number)
45902290627284212541…09299009172213637119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2129239

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 9ab932a17c0212967ef7a8849f8d1bc1e24f9bbc67ac1a773dc9db364e85fde4

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 #2,129,239 on Chainz β†—
Circulating Supply:57,949,421 XPMΒ·at block #6,838,143 Β· updates every 60s
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