Home/Chain Registry/Block #3,226,029

Block #3,226,029

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/15/2019, 7:20:51 AM · Difficulty 11.0049 · 3,612,496 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

643edd289ddc66c4e822292f34e611569e98fbed0bbf2985553c9c64629b4eb3

View on Chainz ↗

Height

#3,226,029

Difficulty

11.004936

Transactions

Size

868 B

Version

Bits

0b014380

Nonce

343,690,218

Timestamp

6/15/2019, 7:20:51 AM

Confirmations

3,612,496

Merkle Root

2cccab4fa9a5a493531da589631c9453e10a4e12ce3245f438fe95da9ea0930d

Transactions (2)

Coinbase674691f0fb88d4…94d47e6443af84

1 in → 1 out8.2500 XPM110 B

AbXwmGxD…4XXYP765

0ab358da5600fb…32b46dd4e786e3

4 in → 2 out257.3811 XPM669 B

AQpirNZH…YMX3K11g AVWqcjJd…EXBEKtEz

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.066 × 10⁹¹(92-digit number)

70664220962100421968…42453022184926984000

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

7.066 × 10⁹¹(92-digit number)

70664220962100421968…42453022184926983999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.066 × 10⁹¹(92-digit number)

70664220962100421968…42453022184926984001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.413 × 10⁹²(93-digit number)

14132844192420084393…84906044369853967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.413 × 10⁹²(93-digit number)

14132844192420084393…84906044369853968001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.826 × 10⁹²(93-digit number)

28265688384840168787…69812088739707935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.826 × 10⁹²(93-digit number)

28265688384840168787…69812088739707936001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

5.653 × 10⁹²(93-digit number)

56531376769680337575…39624177479415871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.653 × 10⁹²(93-digit number)

56531376769680337575…39624177479415872001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.130 × 10⁹³(94-digit number)

11306275353936067515…79248354958831743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.130 × 10⁹³(94-digit number)

11306275353936067515…79248354958831744001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.261 × 10⁹³(94-digit number)

22612550707872135030…58496709917663487999

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — 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 →

★★★☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 3226029

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 643edd289ddc66c4e822292f34e611569e98fbed0bbf2985553c9c64629b4eb3

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 → Debug Window → 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 #3,226,029 on Chainz ↗

Block #3,226,029

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