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Home/Chain Registry/Block #1,512,792

Block #1,512,792

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/26/2016, 7:48:10 AM Β· Difficulty 10.6038 Β· 5,313,359 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
edd8e5be96b0e545dc8f90435f35b6f604cb810ce5eb77eaef6f8a5fe41143a1
View on Chainz β†—

Difficulty

10.603834

Transactions

1

Size

198 B

Version

2

Bits

0a9a94df

Nonce

689,277,480

Timestamp

3/26/2016, 7:48:10 AM

Confirmations

5,313,359

Merkle Root

92fd5a332dec4588b638f48b5c8d9adcc795a407c00c1e7a63ce65849ee8cc50
Transactions (1)
Coinbase92fd5a332dec45…ce65849ee8cc50
1 in β†’ 1 out8.8800 XPM109 B
AGjqsK55…N7hWtKqL
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.

2.952 Γ— 10⁹²(93-digit number)
29528538886376798700…97311011872041891520
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
2.952 Γ— 10⁹²(93-digit number)
29528538886376798700…97311011872041891519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.952 Γ— 10⁹²(93-digit number)
29528538886376798700…97311011872041891521
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
5.905 Γ— 10⁹²(93-digit number)
59057077772753597400…94622023744083783039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.905 Γ— 10⁹²(93-digit number)
59057077772753597400…94622023744083783041
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
1.181 Γ— 10⁹³(94-digit number)
11811415554550719480…89244047488167566079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.181 Γ— 10⁹³(94-digit number)
11811415554550719480…89244047488167566081
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
2.362 Γ— 10⁹³(94-digit number)
23622831109101438960…78488094976335132159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.362 Γ— 10⁹³(94-digit number)
23622831109101438960…78488094976335132161
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
4.724 Γ— 10⁹³(94-digit number)
47245662218202877920…56976189952670264319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.724 Γ— 10⁹³(94-digit number)
47245662218202877920…56976189952670264321
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 1512792

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 edd8e5be96b0e545dc8f90435f35b6f604cb810ce5eb77eaef6f8a5fe41143a1

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 #1,512,792 on Chainz β†—
Circulating Supply:57,853,334 XPMΒ·at block #6,826,150 Β· updates every 60s
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