Block #476,383

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 7:24:45 PM · Difficulty 10.4714 · 6,350,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

993f64eef7481e9384635d1123c2700cac1c1761f1364a9de7e51d4cd27829fe

View on Chainz ↗

Height

#476,383

Difficulty

10.471413

Transactions

Size

1.08 KB

Version

Bits

0a78ae81

Nonce

29,083

Timestamp

4/5/2014, 7:24:45 PM

Confirmations

6,350,571

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

bacb3e82fa70d713b66429ce6be5c2007337bfb037545527448b8f949d048b76

Transactions (5)

Coinbase03ac61443b43b6…cb5b853e0b3114

1 in → 1 out9.1500 XPM116 B

AbwWkWZt…kawDhufa

0fbcc17893e761…b966a49890c816

1 in → 2 out6.6174 XPM225 B

ANZUxYNW…P1pZfYxg APZKNmzm…FPzkv92y

15e066d5433444…765d58ab6fb0a2

1 in → 2 out5.9786 XPM225 B

ANhRsXb5…daZjXU1k AYWUkZZs…NayuGkWu

ac0d754f6d38f0…2964de735970e5

1 in → 2 out5.5749 XPM225 B

AX2ZQsEV…Dq5e7v24 AWP3d7Xe…CqPy4FP4

815abaf412c36b…d2fa763fcdd2a7

1 in → 2 out5.6027 XPM226 B

AGChbYUF…k8wmDUDf AcgFDZVL…poBohqAy

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.

3.012 × 10⁹⁴(95-digit number)

30124340936913121286…07851833372132991999

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

3.012 × 10⁹⁴(95-digit number)

30124340936913121286…07851833372132991999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.012 × 10⁹⁴(95-digit number)

30124340936913121286…07851833372132992001

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

6.024 × 10⁹⁴(95-digit number)

60248681873826242573…15703666744265983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.024 × 10⁹⁴(95-digit number)

60248681873826242573…15703666744265984001

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

1.204 × 10⁹⁵(96-digit number)

12049736374765248514…31407333488531967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.204 × 10⁹⁵(96-digit number)

12049736374765248514…31407333488531968001

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

2.409 × 10⁹⁵(96-digit number)

24099472749530497029…62814666977063935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.409 × 10⁹⁵(96-digit number)

24099472749530497029…62814666977063936001

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

4.819 × 10⁹⁵(96-digit number)

48198945499060994059…25629333954127871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.819 × 10⁹⁵(96-digit number)

48198945499060994059…25629333954127872001

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 #476,383

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