Block #518,748

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 7:25:26 PM · Difficulty 10.8540 · 6,292,413 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d65e8cf98cbe28cc4555d17e25792f5cfaafea1ca232a799984187b0a4a74856

View on Chainz ↗

Height

#518,748

Difficulty

10.853963

Transactions

Size

617 B

Version

Bits

0ada9d5a

Nonce

81,577,158

Timestamp

4/30/2014, 7:25:26 PM

Confirmations

6,292,413

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5fd5dc352ad19bbfdbbba7e01e74fb568e35aa023b5a3f7391c7ad55c351463a

Transactions (2)

Coinbase31388d0ec74d09…069b27f730c547

1 in → 1 out8.4800 XPM116 B

AbwWkWZt…kawDhufa

62b48279d3b725…81643bdfdbd751

2 in → 4 out9.8237 XPM409 B

AHprswVT…7ysvGhPF AZa2QvH4…JvH9i3cj AHXJ1dhk…mhL46N6m AeKNrjNj…1NEq95Ta

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.

6.689 × 10⁹⁸(99-digit number)

66894472322238398043…73725148343846895199

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

6.689 × 10⁹⁸(99-digit number)

66894472322238398043…73725148343846895199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.689 × 10⁹⁸(99-digit number)

66894472322238398043…73725148343846895201

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

1.337 × 10⁹⁹(100-digit number)

13378894464447679608…47450296687693790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.337 × 10⁹⁹(100-digit number)

13378894464447679608…47450296687693790401

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

2.675 × 10⁹⁹(100-digit number)

26757788928895359217…94900593375387580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.675 × 10⁹⁹(100-digit number)

26757788928895359217…94900593375387580801

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

5.351 × 10⁹⁹(100-digit number)

53515577857790718435…89801186750775161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.351 × 10⁹⁹(100-digit number)

53515577857790718435…89801186750775161601

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

1.070 × 10¹⁰⁰(101-digit number)

10703115571558143687…79602373501550323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.070 × 10¹⁰⁰(101-digit number)

10703115571558143687…79602373501550323201

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 #518,748

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