Home/Chain Registry/Block #447,699

Block #447,699

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 10:52:12 AM · Difficulty 10.3610 · 6,343,994 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f86d7a0f7b100ee3a9e6c48642696f4597ab462019b0e1b35272bf0167ef026c

View on Chainz ↗

Height

#447,699

Difficulty

10.361031

Transactions

Size

200 B

Version

Bits

0a5c6c87

Nonce

441,098

Timestamp

3/17/2014, 10:52:12 AM

Confirmations

6,343,994

Merkle Root

a0cfe8027a2e29db7eb64b0d538ae086af050bb70192580f69cf675766630d0f

Transactions (1)

Coinbasea0cfe8027a2e29…cf675766630d0f

1 in → 1 out9.3000 XPM110 B

AeKNrjNj…1NEq95Ta

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.

2.726 × 10⁹⁵(96-digit number)

27265742176159018135…88256861878642931660

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

2.726 × 10⁹⁵(96-digit number)

27265742176159018135…88256861878642931659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.726 × 10⁹⁵(96-digit number)

27265742176159018135…88256861878642931661

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

5.453 × 10⁹⁵(96-digit number)

54531484352318036271…76513723757285863319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.453 × 10⁹⁵(96-digit number)

54531484352318036271…76513723757285863321

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

1.090 × 10⁹⁶(97-digit number)

10906296870463607254…53027447514571726639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.090 × 10⁹⁶(97-digit number)

10906296870463607254…53027447514571726641

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

2.181 × 10⁹⁶(97-digit number)

21812593740927214508…06054895029143453279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.181 × 10⁹⁶(97-digit number)

21812593740927214508…06054895029143453281

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

4.362 × 10⁹⁶(97-digit number)

43625187481854429017…12109790058286906559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.362 × 10⁹⁶(97-digit number)

43625187481854429017…12109790058286906561

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 447699

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 f86d7a0f7b100ee3a9e6c48642696f4597ab462019b0e1b35272bf0167ef026c

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 #447,699 on Chainz ↗