Block #340,341

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 5:30:18 PM · Difficulty 10.1309 · 6,470,112 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd89b7a27fa8fbcc52141c7f158ab5a82ea2414046d99f23299cd59252458e91

View on Chainz ↗

Height

#340,341

Difficulty

10.130897

Transactions

Size

1.01 KB

Version

Bits

0a21827a

Nonce

6,003

Timestamp

1/2/2014, 5:30:18 PM

Confirmations

6,470,112

Mined by

⛏️ u1aR'AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

b2d6cc79f3d7e883b8a32221203583fdde35bc6ab042ad395c913d74f0252a18

Transactions (1)

Coinbaseb2d6cc79f3d7e8…913d74f0252a18

1 in → 26 out9.7299 XPM947 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR AYtDvcGs…VuAcA7m7 AG5YAjec…VhA4Aeh1 AJ19VDo9…9iY1XZAC

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.

1.515 × 10⁹⁷(98-digit number)

15151013996023292837…47925169875793974799

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

1.515 × 10⁹⁷(98-digit number)

15151013996023292837…47925169875793974799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.515 × 10⁹⁷(98-digit number)

15151013996023292837…47925169875793974801

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

3.030 × 10⁹⁷(98-digit number)

30302027992046585674…95850339751587949599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.030 × 10⁹⁷(98-digit number)

30302027992046585674…95850339751587949601

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

6.060 × 10⁹⁷(98-digit number)

60604055984093171348…91700679503175899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.060 × 10⁹⁷(98-digit number)

60604055984093171348…91700679503175899201

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

1.212 × 10⁹⁸(99-digit number)

12120811196818634269…83401359006351798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.212 × 10⁹⁸(99-digit number)

12120811196818634269…83401359006351798401

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

2.424 × 10⁹⁸(99-digit number)

24241622393637268539…66802718012703596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.424 × 10⁹⁸(99-digit number)

24241622393637268539…66802718012703596801

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 #340,341

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