Block #403,179

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2014, 11:48:52 PM · Difficulty 10.4323 · 6,406,247 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b50d1bccea0ccc6309104afc63c42c913a3a75dbbfdb8972904f85417b9358c0

View on Chainz ↗

Height

#403,179

Difficulty

10.432347

Transactions

Size

1.43 KB

Version

Bits

0a6eae4f

Nonce

301,990,803

Timestamp

2/13/2014, 11:48:52 PM

Confirmations

6,406,247

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e6bf0d1e9cd886e21dfbba3241a4df04ef4bdfd35ed000c4d90f948ff67b8462

Transactions (2)

Coinbase51741f33e6c537…d3332017ce09f1

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

f9c09ec7fad583…e38e13a7a8f3ae

8 in → 2 out800.0104 XPM1.23 KB

AdgeMX8n…8V6AsBN6 AdEQNkwU…pzTWiQEM

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.

6.151 × 10⁹⁶(97-digit number)

61510437056190209901…97678379494485160959

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

6.151 × 10⁹⁶(97-digit number)

61510437056190209901…97678379494485160959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.151 × 10⁹⁶(97-digit number)

61510437056190209901…97678379494485160961

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

1.230 × 10⁹⁷(98-digit number)

12302087411238041980…95356758988970321919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.230 × 10⁹⁷(98-digit number)

12302087411238041980…95356758988970321921

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

2.460 × 10⁹⁷(98-digit number)

24604174822476083960…90713517977940643839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.460 × 10⁹⁷(98-digit number)

24604174822476083960…90713517977940643841

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

4.920 × 10⁹⁷(98-digit number)

49208349644952167921…81427035955881287679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.920 × 10⁹⁷(98-digit number)

49208349644952167921…81427035955881287681

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

9.841 × 10⁹⁷(98-digit number)

98416699289904335843…62854071911762575359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.841 × 10⁹⁷(98-digit number)

98416699289904335843…62854071911762575361

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 #403,179

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