Block #404,777

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/15/2014, 2:26:45 AM · Difficulty 10.4328 · 6,399,110 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

479d4ab00f09ebae8aba54eca5e81d696d97f998f9fd118207d8b4ce75cc4057

View on Chainz ↗

Height

#404,777

Difficulty

10.432774

Transactions

Size

3.44 KB

Version

Bits

0a6eca44

Nonce

5,486

Timestamp

2/15/2014, 2:26:45 AM

Confirmations

6,399,110

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

76f61cb4a986ee1852531fa15215899a91986117dfd6ee7cffa712ac9a151f4f

Transactions (5)

Coinbase217de5c5a22bec…4d5c5eefbf68aa

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

e1226c956bc3a4…593d4a9a280d8f

5 in → 11 out31.7815 XPM1022 B

AHXxppsF…jkGkqokY AVE94w5J…WN4TXnY3 AeKNrjNj…1NEq95Ta AMNB6xAZ…5noM4CFx ASxAWksy…kTdbbZET

2d18b44f480122…bdc2370fc047f9

1 in → 2 out7.1247 XPM225 B

AXUM77bz…XVD5jzqL AThAkSeT…LNmHgPc6

4b6eca754789ef…54b388d35c3d77

10 in → 2 out5.0282 XPM1.52 KB

ALhvUF1m…HRV7Un9k AGAuDbuA…ed3nVPFw

e55965a2f63e41…46ed2985798348

3 in → 2 out1.0144 XPM521 B

AHAb2cgs…v1BxfcCa ASAJTqw7…mmuix2Cd

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.

7.870 × 10⁹⁶(97-digit number)

78703847027128496417…66794220045685955879

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

7.870 × 10⁹⁶(97-digit number)

78703847027128496417…66794220045685955879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.870 × 10⁹⁶(97-digit number)

78703847027128496417…66794220045685955881

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

1.574 × 10⁹⁷(98-digit number)

15740769405425699283…33588440091371911759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.574 × 10⁹⁷(98-digit number)

15740769405425699283…33588440091371911761

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

3.148 × 10⁹⁷(98-digit number)

31481538810851398566…67176880182743823519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.148 × 10⁹⁷(98-digit number)

31481538810851398566…67176880182743823521

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

6.296 × 10⁹⁷(98-digit number)

62963077621702797133…34353760365487647039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.296 × 10⁹⁷(98-digit number)

62963077621702797133…34353760365487647041

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

1.259 × 10⁹⁸(99-digit number)

12592615524340559426…68707520730975294079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.259 × 10⁹⁸(99-digit number)

12592615524340559426…68707520730975294081

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