Block #476,360

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 6:56:50 PM · Difficulty 10.4718 · 6,321,261 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7025c33077fc81365d18ce13ec9d331f1b10e53365b6d396aa5ca0214edf7720

View on Chainz ↗

Height

#476,360

Difficulty

10.471841

Transactions

Size

1.59 KB

Version

Bits

0a78ca92

Nonce

52,534,559

Timestamp

4/5/2014, 6:56:50 PM

Confirmations

6,321,261

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c0507ffed639fca481947ad375f0a53ea8afc0f8e5a2a5ee282e511cad23fad4

Transactions (2)

Coinbase824fb7af5cfba4…36044f785d7d31

1 in → 1 out9.1300 XPM116 B

AbwWkWZt…kawDhufa

84b8de970c1675…549819314c530f

7 in → 17 out56.2991 XPM1.38 KB

AYKqvL9i…9eGuiBEs AR7n9chB…ozyWpotN AUQ1jCaq…CiXqzwJB AeKNrjNj…1NEq95Ta AbY6jpKm…xfyDrP1G

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.

1.450 × 10⁹⁷(98-digit number)

14501205906940732201…15160605571949601149

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

1.450 × 10⁹⁷(98-digit number)

14501205906940732201…15160605571949601149

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.450 × 10⁹⁷(98-digit number)

14501205906940732201…15160605571949601151

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

2.900 × 10⁹⁷(98-digit number)

29002411813881464403…30321211143899202299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.900 × 10⁹⁷(98-digit number)

29002411813881464403…30321211143899202301

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

5.800 × 10⁹⁷(98-digit number)

58004823627762928807…60642422287798404599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.800 × 10⁹⁷(98-digit number)

58004823627762928807…60642422287798404601

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

1.160 × 10⁹⁸(99-digit number)

11600964725552585761…21284844575596809199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.160 × 10⁹⁸(99-digit number)

11600964725552585761…21284844575596809201

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

2.320 × 10⁹⁸(99-digit number)

23201929451105171522…42569689151193618399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.320 × 10⁹⁸(99-digit number)

23201929451105171522…42569689151193618401

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