Block #251,069

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 7:56:11 PM · Difficulty 9.9694 · 6,563,960 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

12c9ee358633f2a169a930decf97e13bf1c26dd78b19bedf90145b6988c0a0c3

View on Chainz ↗

Height

#251,069

Difficulty

9.969407

Transactions

Size

424 B

Version

Bits

09f82b0d

Nonce

12,880

Timestamp

11/8/2013, 7:56:11 PM

Confirmations

6,563,960

Mined by

⛏️ P2SHAPLnkgnLaSv5GyqvZ6quLMJdRouJrZCRsA

Merkle Root

4300205d95e5d95e89f3504a9fe11f50a81716863438b2be1a7ca6b10dcfe742

Transactions (2)

Coinbase09a42c7fecc893…493afa19223313

1 in → 1 out10.0600 XPM109 B

APLnkgnL…uJrZCRsA

775e264b7cfed3…3b5d0b637ae0a5

1 in → 2 out93.2533 XPM226 B

AZdmkNt9…Dk8ffFeU AQG1Upws…aq5RrWHY

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.

3.910 × 10⁹¹(92-digit number)

39109050266726136719…95196402603307549999

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

3.910 × 10⁹¹(92-digit number)

39109050266726136719…95196402603307549999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.910 × 10⁹¹(92-digit number)

39109050266726136719…95196402603307550001

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

7.821 × 10⁹¹(92-digit number)

78218100533452273439…90392805206615099999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.821 × 10⁹¹(92-digit number)

78218100533452273439…90392805206615100001

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

1.564 × 10⁹²(93-digit number)

15643620106690454687…80785610413230199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.564 × 10⁹²(93-digit number)

15643620106690454687…80785610413230200001

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

3.128 × 10⁹²(93-digit number)

31287240213380909375…61571220826460399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.128 × 10⁹²(93-digit number)

31287240213380909375…61571220826460400001

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

6.257 × 10⁹²(93-digit number)

62574480426761818751…23142441652920799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.257 × 10⁹²(93-digit number)

62574480426761818751…23142441652920800001

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 #251,069

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