Block #287,940

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 1:01:51 PM · Difficulty 9.9872 · 6,522,033 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0483d2d1f64bfbe75013c463bed4180f2a5d67cc8bea34ec1b6a6de2f6fff785

View on Chainz ↗

Height

#287,940

Difficulty

9.987194

Transactions

Size

1.18 KB

Version

Bits

09fcb8bb

Nonce

1,170

Timestamp

12/1/2013, 1:01:51 PM

Confirmations

6,522,033

Mined by

⛏️ daR35AGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

d1fbb3131bc9f4bf2e0a82e27959d521c386557c16fa92f1af0f04393dbcd01f

Transactions (1)

Coinbased1fbb3131bc9f4…0f04393dbcd01f

1 in → 31 out9.9900 XPM1.09 KB

AGFAJ5YL…ZEnBbk6G ANQKf2g4…29NaVj23 AMdvB6BS…DPq9FYdA Ac6mGvmQ…XqWmPHjR AHLsU39G…fiNcno66

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.

3.418 × 10⁹⁴(95-digit number)

34189199259723930851…66007789616393526399

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

3.418 × 10⁹⁴(95-digit number)

34189199259723930851…66007789616393526399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.418 × 10⁹⁴(95-digit number)

34189199259723930851…66007789616393526401

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

6.837 × 10⁹⁴(95-digit number)

68378398519447861703…32015579232787052799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.837 × 10⁹⁴(95-digit number)

68378398519447861703…32015579232787052801

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

1.367 × 10⁹⁵(96-digit number)

13675679703889572340…64031158465574105599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.367 × 10⁹⁵(96-digit number)

13675679703889572340…64031158465574105601

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

2.735 × 10⁹⁵(96-digit number)

27351359407779144681…28062316931148211199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.735 × 10⁹⁵(96-digit number)

27351359407779144681…28062316931148211201

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

5.470 × 10⁹⁵(96-digit number)

54702718815558289362…56124633862296422399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.470 × 10⁹⁵(96-digit number)

54702718815558289362…56124633862296422401

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 #287,940

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