Block #436,477

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 2:55:26 PM · Difficulty 10.3607 · 6,376,149 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3f374f6d663978d803a9b743b7db3f0b0cd04d2c374dfdfc00039d07080b640

View on Chainz ↗

Height

#436,477

Difficulty

10.360749

Transactions

Size

968 B

Version

Bits

0a5c5a12

Nonce

63,197

Timestamp

3/9/2014, 2:55:26 PM

Confirmations

6,376,149

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ca366aa4d7e635abaaf54f0683bd47e7f6f8965fadcbdc0c98242dea123f7831

Transactions (1)

Coinbaseca366aa4d7e635…242dea123f7831

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

7.328 × 10⁹¹(92-digit number)

73282291697183740314…73272358300015537169

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

7.328 × 10⁹¹(92-digit number)

73282291697183740314…73272358300015537169

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.328 × 10⁹¹(92-digit number)

73282291697183740314…73272358300015537171

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

1.465 × 10⁹²(93-digit number)

14656458339436748062…46544716600031074339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.465 × 10⁹²(93-digit number)

14656458339436748062…46544716600031074341

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

2.931 × 10⁹²(93-digit number)

29312916678873496125…93089433200062148679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.931 × 10⁹²(93-digit number)

29312916678873496125…93089433200062148681

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

5.862 × 10⁹²(93-digit number)

58625833357746992251…86178866400124297359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.862 × 10⁹²(93-digit number)

58625833357746992251…86178866400124297361

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

1.172 × 10⁹³(94-digit number)

11725166671549398450…72357732800248594719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.172 × 10⁹³(94-digit number)

11725166671549398450…72357732800248594721

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 #436,477

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