Block #364,325

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 11:57:07 PM · Difficulty 10.4219 · 6,441,930 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa048e195c5cf40501008541eef399e98363c3ba86ac31345c04484241912ce3

View on Chainz ↗

Height

#364,325

Difficulty

10.421896

Transactions

Size

1.42 KB

Version

Bits

0a6c015a

Nonce

201,047

Timestamp

1/17/2014, 11:57:07 PM

Confirmations

6,441,930

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

eb2b023a6c6e586bb976d70b4644f439fc230b55a51a39b4ac06052f17def21c

Transactions (3)

Coinbaseef3762c016345c…f9fa1bd9cdaaff

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

a194388fa99b39…c4692ea32e1772

5 in → 13 out38.0081 XPM1.03 KB

AMFS2EAK…iMaSK3nV AXwoC6Y4…Bb3zMSZ2 APQCLq5D…cpNbYpoy AY1FuBSV…jEZrVd1U AcBnBiUw…CYFN81QZ

3805f103c3905f…d81b8d024a25bf

1 in → 1 out3.0823 XPM193 B

AQuow7cX…TF1HcP7V

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.

3.002 × 10⁹⁸(99-digit number)

30026452821748418420…70591784774611187199

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

3.002 × 10⁹⁸(99-digit number)

30026452821748418420…70591784774611187199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.002 × 10⁹⁸(99-digit number)

30026452821748418420…70591784774611187201

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

6.005 × 10⁹⁸(99-digit number)

60052905643496836840…41183569549222374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.005 × 10⁹⁸(99-digit number)

60052905643496836840…41183569549222374401

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

1.201 × 10⁹⁹(100-digit number)

12010581128699367368…82367139098444748799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.201 × 10⁹⁹(100-digit number)

12010581128699367368…82367139098444748801

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

2.402 × 10⁹⁹(100-digit number)

24021162257398734736…64734278196889497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.402 × 10⁹⁹(100-digit number)

24021162257398734736…64734278196889497601

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

4.804 × 10⁹⁹(100-digit number)

48042324514797469472…29468556393778995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.804 × 10⁹⁹(100-digit number)

48042324514797469472…29468556393778995201

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 #364,325

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