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Block #326,816

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 2:10:41 AM · Difficulty 10.1852 · 6,498,891 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5c677f5b8b524b20aee24e1e00c7be847f1edd7f2e775dd49ebb3eba18f2e02

View on Chainz ↗

Height

#326,816

Difficulty

10.185212

Transactions

Size

1.05 KB

Version

Bits

0a2f6a09

Nonce

6,660

Timestamp

12/24/2013, 2:10:41 AM

Confirmations

6,498,891

Merkle Root

3a153eaa122d26fa54bd45c7f9c82fdae16c16ed3d9d1f35bd642401c58ce3f0

Transactions (1)

Coinbase3a153eaa122d26…642401c58ce3f0

1 in → 27 out9.6200 XPM981 B

Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AdwTEXyC…NwbVbqZV

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.

3.574 × 10⁹⁶(97-digit number)

35744360850344446027…94420725728966110560

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

3.574 × 10⁹⁶(97-digit number)

35744360850344446027…94420725728966110559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.574 × 10⁹⁶(97-digit number)

35744360850344446027…94420725728966110561

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

7.148 × 10⁹⁶(97-digit number)

71488721700688892054…88841451457932221119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.148 × 10⁹⁶(97-digit number)

71488721700688892054…88841451457932221121

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

1.429 × 10⁹⁷(98-digit number)

14297744340137778410…77682902915864442239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.429 × 10⁹⁷(98-digit number)

14297744340137778410…77682902915864442241

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

2.859 × 10⁹⁷(98-digit number)

28595488680275556821…55365805831728884479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.859 × 10⁹⁷(98-digit number)

28595488680275556821…55365805831728884481

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

5.719 × 10⁹⁷(98-digit number)

57190977360551113643…10731611663457768959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.719 × 10⁹⁷(98-digit number)

57190977360551113643…10731611663457768961

Verify on FactorDB ↗Wolfram Alpha ↗

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

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 — 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

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 × 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 326816

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 f5c677f5b8b524b20aee24e1e00c7be847f1edd7f2e775dd49ebb3eba18f2e02

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 #326,816 on Chainz ↗

Block #326,816

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