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Home/Chain Registry/Block #2,646,311

Block #2,646,311

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 7:27:53 AM Β· Difficulty 11.7480 Β· 4,195,948 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ae9665a6c6db8f73f9ab00f5fec8b2abb647a2f9a97f2e8f69842aee606e4d4
View on Chainz β†—

Difficulty

11.748002

Transactions

1

Size

199 B

Version

2

Bits

0bbf7d0d

Nonce

2,857,659

Timestamp

5/3/2018, 7:27:53 AM

Confirmations

4,195,948

Merkle Root

c097a742e019f2bfd4c8e09d4920b09168ca81622e098a2a6a353d86b84d2b84
Transactions (1)
Coinbasec097a742e019f2…353d86b84d2b84
1 in β†’ 1 out7.2300 XPM109 B
AVd8pBdE…bKfBYtGe
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.

2.679 Γ— 10⁹⁡(96-digit number)
26798919320263490590…56959580420463964160
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
2.679 Γ— 10⁹⁡(96-digit number)
26798919320263490590…56959580420463964159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.679 Γ— 10⁹⁡(96-digit number)
26798919320263490590…56959580420463964161
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
5.359 Γ— 10⁹⁡(96-digit number)
53597838640526981181…13919160840927928319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.359 Γ— 10⁹⁡(96-digit number)
53597838640526981181…13919160840927928321
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
1.071 Γ— 10⁹⁢(97-digit number)
10719567728105396236…27838321681855856639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.071 Γ— 10⁹⁢(97-digit number)
10719567728105396236…27838321681855856641
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
2.143 Γ— 10⁹⁢(97-digit number)
21439135456210792472…55676643363711713279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.143 Γ— 10⁹⁢(97-digit number)
21439135456210792472…55676643363711713281
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
4.287 Γ— 10⁹⁢(97-digit number)
42878270912421584945…11353286727423426559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.287 Γ— 10⁹⁢(97-digit number)
42878270912421584945…11353286727423426561
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
8.575 Γ— 10⁹⁢(97-digit number)
85756541824843169890…22706573454846853119
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 2646311

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 9ae9665a6c6db8f73f9ab00f5fec8b2abb647a2f9a97f2e8f69842aee606e4d4

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 #2,646,311 on Chainz β†—
Circulating Supply:57,982,470 XPMΒ·at block #6,842,258 Β· updates every 60s
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