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Home/Chain Registry/Block #2,668,868

Block #2,668,868

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/19/2018, 8:36:14 PM Β· Difficulty 11.6768 Β· 4,171,783 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d5cea8cd041dc5d693fc9cb9012fa92f17bdd447c67ea2b3053b716008b83db
View on Chainz β†—

Difficulty

11.676807

Transactions

1

Size

200 B

Version

2

Bits

0bad4337

Nonce

1,879,176,873

Timestamp

5/19/2018, 8:36:14 PM

Confirmations

4,171,783

Merkle Root

73f9224e03edc0df18c70c34c35480d04764d295b233cdfdfe8906cfdb4dcc62
Transactions (1)
Coinbase73f9224e03edc0…8906cfdb4dcc62
1 in β†’ 1 out7.3200 XPM110 B
AGxyVX6X…QBL5WvkJ
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.

6.743 Γ— 10⁹⁴(95-digit number)
67439293367527365959…07121706720139771360
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
6.743 Γ— 10⁹⁴(95-digit number)
67439293367527365959…07121706720139771359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.743 Γ— 10⁹⁴(95-digit number)
67439293367527365959…07121706720139771361
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
1.348 Γ— 10⁹⁡(96-digit number)
13487858673505473191…14243413440279542719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.348 Γ— 10⁹⁡(96-digit number)
13487858673505473191…14243413440279542721
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
2.697 Γ— 10⁹⁡(96-digit number)
26975717347010946383…28486826880559085439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.697 Γ— 10⁹⁡(96-digit number)
26975717347010946383…28486826880559085441
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
5.395 Γ— 10⁹⁡(96-digit number)
53951434694021892767…56973653761118170879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.395 Γ— 10⁹⁡(96-digit number)
53951434694021892767…56973653761118170881
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
1.079 Γ— 10⁹⁢(97-digit number)
10790286938804378553…13947307522236341759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.079 Γ— 10⁹⁢(97-digit number)
10790286938804378553…13947307522236341761
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
2.158 Γ— 10⁹⁢(97-digit number)
21580573877608757107…27894615044472683519
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 2668868

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 4d5cea8cd041dc5d693fc9cb9012fa92f17bdd447c67ea2b3053b716008b83db

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 #2,668,868 on Chainz β†—
Circulating Supply:57,969,551 XPMΒ·at block #6,840,650 Β· updates every 60s
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