Home/Chain Registry/Block #221,681

Block #221,681

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 5:07:41 PM · Difficulty 9.9396 · 6,616,547 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40e9839b21dc0ca1aa8a63f5f5deb788fe0f1ac76a46d3c6536fd51dda450416

View on Chainz ↗

Height

#221,681

Difficulty

9.939582

Transactions

Size

1.66 KB

Version

Bits

09f08878

Nonce

185,005

Timestamp

10/21/2013, 5:07:41 PM

Confirmations

6,616,547

Merkle Root

1893797d9bca0a2c5a40e0abee4a46f57b58031758fd72c86b58efb880c0cf54

Transactions (2)

Coinbasec858f0a8f0413e…8002ea1d19a74c

1 in → 40 out10.0900 XPM1.39 KB

AeckU1Kq…a9chH61d AKXeSXzu…yeuNjvhB AcMPa5Yh…j5yHgkwm AJKYzp1g…SvZiepke AP5d2TUf…P2wUZ8fL

d83585968b7887…9c80ada7b54393

1 in → 2 out10.1800 XPM192 B

AX73dxCy…fMsyAg1C AQAvQSWZ…C9mFkvux

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.

1.990 × 10⁹⁵(96-digit number)

19904556544508050476…12060626481368625920

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

1.990 × 10⁹⁵(96-digit number)

19904556544508050476…12060626481368625919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.990 × 10⁹⁵(96-digit number)

19904556544508050476…12060626481368625921

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

3.980 × 10⁹⁵(96-digit number)

39809113089016100952…24121252962737251839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.980 × 10⁹⁵(96-digit number)

39809113089016100952…24121252962737251841

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

7.961 × 10⁹⁵(96-digit number)

79618226178032201905…48242505925474503679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.961 × 10⁹⁵(96-digit number)

79618226178032201905…48242505925474503681

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

1.592 × 10⁹⁶(97-digit number)

15923645235606440381…96485011850949007359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.592 × 10⁹⁶(97-digit number)

15923645235606440381…96485011850949007361

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

3.184 × 10⁹⁶(97-digit number)

31847290471212880762…92970023701898014719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 221681

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 40e9839b21dc0ca1aa8a63f5f5deb788fe0f1ac76a46d3c6536fd51dda450416

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 #221,681 on Chainz ↗

Block #221,681

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