Block #247,659

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 9:39:19 PM · Difficulty 9.9653 · 6,548,859 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5ec36cb3c2732df5dd05176d73594fdbc8f89a4b959f6ecb2f5cfdb6e1d7bb6d

View on Chainz ↗

Height

#247,659

Difficulty

9.965258

Transactions

Size

1.74 KB

Version

Bits

09f71b29

Nonce

443,313

Timestamp

11/6/2013, 9:39:19 PM

Confirmations

6,548,859

Mined by

⛏️ kRzARpndEmcGyFUFhdFVbgqJiPBAmHg792kEk

Merkle Root

430334bcc7ae726c55c28adb4cda0355be97f2879f3015c3ccc327262c8a6337

Transactions (1)

Coinbase430334bcc7ae72…c327262c8a6337

1 in → 48 out10.0300 XPM1.65 KB

ARpndEmc…Hg792kEk AdnG9gQ7…N9B7mA2p AZrPRT4s…Pz2AcjLi AXRun4Jx…ReRaSdaU AGbRhLj1…nZcEQFqQ

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.

4.790 × 10⁹⁴(95-digit number)

47900675769907438495…04919887645024524499

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

4.790 × 10⁹⁴(95-digit number)

47900675769907438495…04919887645024524499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.790 × 10⁹⁴(95-digit number)

47900675769907438495…04919887645024524501

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

9.580 × 10⁹⁴(95-digit number)

95801351539814876990…09839775290049048999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.580 × 10⁹⁴(95-digit number)

95801351539814876990…09839775290049049001

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

1.916 × 10⁹⁵(96-digit number)

19160270307962975398…19679550580098097999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.916 × 10⁹⁵(96-digit number)

19160270307962975398…19679550580098098001

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

3.832 × 10⁹⁵(96-digit number)

38320540615925950796…39359101160196195999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.832 × 10⁹⁵(96-digit number)

38320540615925950796…39359101160196196001

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

7.664 × 10⁹⁵(96-digit number)

76641081231851901592…78718202320392391999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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