Block #379,309

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 11:09:34 AM · Difficulty 10.4158 · 6,429,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

daf88c292b7794ceebbb467662aa043e9dd5417ce3f8a50af801981e52579456

View on Chainz ↗

Height

#379,309

Difficulty

10.415787

Transactions

Size

1.08 KB

Version

Bits

0a6a7105

Nonce

87,594

Timestamp

1/28/2014, 11:09:34 AM

Confirmations

6,429,464

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

8c9047e77e72cd92c28341e599bceebe189f70b1374a8769665fc3611bb6f293

Transactions (5)

Coinbase94acbd915ed1c7…d94170b274c819

1 in → 1 out9.2400 XPM110 B

AeKNrjNj…1NEq95Ta

914fdf61bbb38c…20882898f7aa6e

1 in → 2 out9.1800 XPM227 B

AFs5WYFF…rJmcQWgK AMU8nEj9…Eo32pqxr

67c43256ecefaa…3b8256195f58eb

1 in → 2 out9.1800 XPM225 B

AXZpvw4S…KkMimbwy AYuAJDNA…Ynx1e6Ko

d8ad62c48fb5f6…571b841fe94221

1 in → 2 out9.1800 XPM226 B

AUQ7Zz7P…qYuYM9vZ ASfQj9Pb…Q87HBF2g

b16b2ee6bc2e89…0eaa2303233368

1 in → 2 out9.1800 XPM227 B

AHHmR85y…uEUgHRhd Aea9xsrR…jHywGb6x

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.

1.017 × 10⁹⁸(99-digit number)

10179926743538089244…08275371226770931199

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

1.017 × 10⁹⁸(99-digit number)

10179926743538089244…08275371226770931199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.017 × 10⁹⁸(99-digit number)

10179926743538089244…08275371226770931201

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

2.035 × 10⁹⁸(99-digit number)

20359853487076178488…16550742453541862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.035 × 10⁹⁸(99-digit number)

20359853487076178488…16550742453541862401

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

4.071 × 10⁹⁸(99-digit number)

40719706974152356977…33101484907083724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.071 × 10⁹⁸(99-digit number)

40719706974152356977…33101484907083724801

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

8.143 × 10⁹⁸(99-digit number)

81439413948304713955…66202969814167449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.143 × 10⁹⁸(99-digit number)

81439413948304713955…66202969814167449601

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

1.628 × 10⁹⁹(100-digit number)

16287882789660942791…32405939628334899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.628 × 10⁹⁹(100-digit number)

16287882789660942791…32405939628334899201

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Cross-reference on Chainz Explorer

Block #379,309

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