Home/Chain Registry/Block #469,224

Block #469,224

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 2:00:38 AM · Difficulty 10.4285 · 6,321,854 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b40fd42000f8afb5b1e9d7d8aca52c1a1e0086fc3c8b2579518760365f3e729e

View on Chainz ↗

Height

#469,224

Difficulty

10.428535

Transactions

Size

2.30 KB

Version

Bits

0a6db472

Nonce

9,955

Timestamp

4/1/2014, 2:00:38 AM

Confirmations

6,321,854

Merkle Root

347650e25910f7079ac05a9c5a3fde69b86f2f5dc6bbb2b7120ca0f9400efdf4

Transactions (4)

Coinbase7dea3858ed7187…552e7477e20d76

1 in → 23 out9.1800 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AScAzqGc…BZ6tV1vJ

9b6547dcd67ce5…08dece9351dd47

1 in → 2 out10.3394 XPM226 B

AV6axBpj…CR71KMpM AL7194fk…YNQBVjTB

5b9e81fc2b23e8…20836d057bcb8a

5 in → 2 out30.1097 XPM819 B

AcECxWxq…LTW8QukW AMB491YH…qXN4yJep

65ac91a5ec00aa…01f115e7cf1246

2 in → 2 out15.4379 XPM374 B

AMo4xYNR…6LV3Le7K AUvG5P2F…5XWYtgDp

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.

3.227 × 10⁹⁶(97-digit number)

32276018368330915759…22048250380319555400

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

3.227 × 10⁹⁶(97-digit number)

32276018368330915759…22048250380319555399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.227 × 10⁹⁶(97-digit number)

32276018368330915759…22048250380319555401

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

6.455 × 10⁹⁶(97-digit number)

64552036736661831519…44096500760639110799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.455 × 10⁹⁶(97-digit number)

64552036736661831519…44096500760639110801

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

1.291 × 10⁹⁷(98-digit number)

12910407347332366303…88193001521278221599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.291 × 10⁹⁷(98-digit number)

12910407347332366303…88193001521278221601

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

2.582 × 10⁹⁷(98-digit number)

25820814694664732607…76386003042556443199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.582 × 10⁹⁷(98-digit number)

25820814694664732607…76386003042556443201

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

5.164 × 10⁹⁷(98-digit number)

51641629389329465215…52772006085112886399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.164 × 10⁹⁷(98-digit number)

51641629389329465215…52772006085112886401

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 469224

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 b40fd42000f8afb5b1e9d7d8aca52c1a1e0086fc3c8b2579518760365f3e729e

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 #469,224 on Chainz ↗