Block #396,576

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 12:06:37 PM · Difficulty 10.4138 · 6,420,708 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

82ea6cecd73820171998b2ab781d0691b2f8705a278fb32c15fc7f14d5bd0765

View on Chainz ↗

Height

#396,576

Difficulty

10.413777

Transactions

Size

433 B

Version

Bits

0a69ed43

Nonce

92,023

Timestamp

2/9/2014, 12:06:37 PM

Confirmations

6,420,708

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

dd0c46780ba6108f93ff9a6de7fc5af1d87dd896c4bac41dacec2cc568e9adf0

Transactions (2)

Coinbase51a456cf717edb…6dd69c5faf5da9

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

f46b73f974b0c4…9578f80f46f918

1 in → 2 out7040.6609 XPM226 B

AZ91HrUE…34yD2F1P ARZaJzLP…QQdGGoca

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.

2.095 × 10⁹⁷(98-digit number)

20956283555475712376…20238464483808678319

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

2.095 × 10⁹⁷(98-digit number)

20956283555475712376…20238464483808678319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.095 × 10⁹⁷(98-digit number)

20956283555475712376…20238464483808678321

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

4.191 × 10⁹⁷(98-digit number)

41912567110951424752…40476928967617356639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.191 × 10⁹⁷(98-digit number)

41912567110951424752…40476928967617356641

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

8.382 × 10⁹⁷(98-digit number)

83825134221902849504…80953857935234713279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.382 × 10⁹⁷(98-digit number)

83825134221902849504…80953857935234713281

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

1.676 × 10⁹⁸(99-digit number)

16765026844380569900…61907715870469426559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.676 × 10⁹⁸(99-digit number)

16765026844380569900…61907715870469426561

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

3.353 × 10⁹⁸(99-digit number)

33530053688761139801…23815431740938853119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.353 × 10⁹⁸(99-digit number)

33530053688761139801…23815431740938853121

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 #396,576

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