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Block #432,539

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/6/2014, 11:33:30 PM · Difficulty 10.3416 · 6,370,658 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72cf05c7366e6749fe82722906445e3437b9c35997cbcd15ae950d145f5e100a

View on Chainz ↗

Height

#432,539

Difficulty

10.341603

Transactions

Size

902 B

Version

Bits

0a577346

Nonce

44,008

Timestamp

3/6/2014, 11:33:30 PM

Confirmations

6,370,658

Merkle Root

cc668bfda5e2dbcde43c05746b7327a4c8f5c0af160332bb8c1add2fa0b582cb

Transactions (1)

Coinbasecc668bfda5e2db…1add2fa0b582cb

1 in → 22 out9.3400 XPM811 B

Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AFutDVqJ…TJTJj6UF

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.

1.324 × 10⁹⁶(97-digit number)

13247166046859105627…95730475001071160320

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

1.324 × 10⁹⁶(97-digit number)

13247166046859105627…95730475001071160319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.324 × 10⁹⁶(97-digit number)

13247166046859105627…95730475001071160321

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

2.649 × 10⁹⁶(97-digit number)

26494332093718211254…91460950002142320639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.649 × 10⁹⁶(97-digit number)

26494332093718211254…91460950002142320641

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

5.298 × 10⁹⁶(97-digit number)

52988664187436422508…82921900004284641279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.298 × 10⁹⁶(97-digit number)

52988664187436422508…82921900004284641281

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

1.059 × 10⁹⁷(98-digit number)

10597732837487284501…65843800008569282559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.059 × 10⁹⁷(98-digit number)

10597732837487284501…65843800008569282561

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

2.119 × 10⁹⁷(98-digit number)

21195465674974569003…31687600017138565119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.119 × 10⁹⁷(98-digit number)

21195465674974569003…31687600017138565121

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

4.239 × 10⁹⁷(98-digit number)

42390931349949138006…63375200034277130239

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 432539

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 72cf05c7366e6749fe82722906445e3437b9c35997cbcd15ae950d145f5e100a

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 #432,539 on Chainz ↗