Block #384,171

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/31/2014, 10:09:05 PM · Difficulty 10.4038 · 6,424,743 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

22ac5fc3cfdb4fe36f2109fab212b3e83b56d4044d828de4bbe14a59a9524642

View on Chainz ↗

Height

#384,171

Difficulty

10.403763

Transactions

Size

971 B

Version

Bits

0a675d05

Nonce

7,064

Timestamp

1/31/2014, 10:09:05 PM

Confirmations

6,424,743

Mined by

⛏️ aR#AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3df3bdf37eaa3bdd5db8ed5562d7c76fe49fb3524a7653f2b01f1a7238a536dc

Transactions (1)

Coinbase3df3bdf37eaa3b…1f1a7238a536dc

1 in → 24 out9.2200 XPM879 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH AJzWx2VD…j4ZSMit5 ARSeozDw…C9HtARnj

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.

5.086 × 10⁹⁸(99-digit number)

50861314407747001495…97185857566564984319

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

5.086 × 10⁹⁸(99-digit number)

50861314407747001495…97185857566564984319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.086 × 10⁹⁸(99-digit number)

50861314407747001495…97185857566564984321

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

1.017 × 10⁹⁹(100-digit number)

10172262881549400299…94371715133129968639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.017 × 10⁹⁹(100-digit number)

10172262881549400299…94371715133129968641

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

2.034 × 10⁹⁹(100-digit number)

20344525763098800598…88743430266259937279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.034 × 10⁹⁹(100-digit number)

20344525763098800598…88743430266259937281

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

4.068 × 10⁹⁹(100-digit number)

40689051526197601196…77486860532519874559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.068 × 10⁹⁹(100-digit number)

40689051526197601196…77486860532519874561

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

8.137 × 10⁹⁹(100-digit number)

81378103052395202392…54973721065039749119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.137 × 10⁹⁹(100-digit number)

81378103052395202392…54973721065039749121

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 #384,171

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