Block #368,978

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 2:15:30 AM · Difficulty 10.4451 · 6,441,347 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6b3eac254ecab340d3a12aaa879f78e900c9c6a5250342d1675e234ac4749c4

View on Chainz ↗

Height

#368,978

Difficulty

10.445137

Transactions

Size

1.45 KB

Version

Bits

0a71f47a

Nonce

5,339

Timestamp

1/21/2014, 2:15:30 AM

Confirmations

6,441,347

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

91715ef13ddb2d4de5cf3dbee9fcc4198d05c2172e05a9d339637e13370577d9

Transactions (2)

Coinbased563db8b003b86…acfa9c0d79e341

1 in → 1 out9.1700 XPM116 B

AbwWkWZt…kawDhufa

528fde85f65e1c…9fea7a6f46c458

6 in → 16 out48.3230 XPM1.24 KB

AJYnjwa1…gJuspnns AeKNrjNj…1NEq95Ta Aaw3phCR…9mHC1CxX ALMMvdpq…tmdBdKKs ATnofWiZ…EmYpDvjZ

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.

3.149 × 10⁹⁸(99-digit number)

31499998606203138072…86007090285038337279

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

3.149 × 10⁹⁸(99-digit number)

31499998606203138072…86007090285038337279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.149 × 10⁹⁸(99-digit number)

31499998606203138072…86007090285038337281

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

6.299 × 10⁹⁸(99-digit number)

62999997212406276144…72014180570076674559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.299 × 10⁹⁸(99-digit number)

62999997212406276144…72014180570076674561

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

1.259 × 10⁹⁹(100-digit number)

12599999442481255228…44028361140153349119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.259 × 10⁹⁹(100-digit number)

12599999442481255228…44028361140153349121

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

2.519 × 10⁹⁹(100-digit number)

25199998884962510457…88056722280306698239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.519 × 10⁹⁹(100-digit number)

25199998884962510457…88056722280306698241

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

5.039 × 10⁹⁹(100-digit number)

50399997769925020915…76113444560613396479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.039 × 10⁹⁹(100-digit number)

50399997769925020915…76113444560613396481

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 #368,978

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