Block #487,334

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 2:25:04 AM · Difficulty 10.6391 · 6,330,293 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29787ae292809b205994900f69e65ca70938d699d0d6b502e57f811b18bdb23c

View on Chainz ↗

Height

#487,334

Difficulty

10.639132

Transactions

Size

901 B

Version

Bits

0aa39e2e

Nonce

58,670

Timestamp

4/12/2014, 2:25:04 AM

Confirmations

6,330,293

Mined by

⛏️ oAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

9666c121d69258e39af78923178b20ba0c564f7abf0cb1291a0371e7eff48b9a

Transactions (1)

Coinbase9666c121d69258…0371e7eff48b9a

1 in → 22 out8.8200 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb AdoqUYAy…tJ482T9b ASgUri65…C7NLcyBg

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.

2.380 × 10⁹³(94-digit number)

23802335475846854501…69161845300210311039

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

2.380 × 10⁹³(94-digit number)

23802335475846854501…69161845300210311039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.380 × 10⁹³(94-digit number)

23802335475846854501…69161845300210311041

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

4.760 × 10⁹³(94-digit number)

47604670951693709002…38323690600420622079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.760 × 10⁹³(94-digit number)

47604670951693709002…38323690600420622081

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

9.520 × 10⁹³(94-digit number)

95209341903387418004…76647381200841244159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.520 × 10⁹³(94-digit number)

95209341903387418004…76647381200841244161

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

1.904 × 10⁹⁴(95-digit number)

19041868380677483600…53294762401682488319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.904 × 10⁹⁴(95-digit number)

19041868380677483600…53294762401682488321

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

3.808 × 10⁹⁴(95-digit number)

38083736761354967201…06589524803364976639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.808 × 10⁹⁴(95-digit number)

38083736761354967201…06589524803364976641

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 #487,334

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