Block #506,639

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 5:32:48 AM · Difficulty 10.8141 · 6,299,223 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0cefed147258dafc23bc31a752308311869fc90bdf8bd513c97b6ea77df32430

View on Chainz ↗

Height

#506,639

Difficulty

10.814105

Transactions

Size

695 B

Version

Bits

0ad06932

Nonce

294,606,909

Timestamp

4/23/2014, 5:32:48 AM

Confirmations

6,299,223

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6e6b5c6c38b8316e02d8157a297c19328d0ef75136cb7f3aa6c3b90f8b7de4ce

Transactions (2)

Coinbase9a50db5818bb3a…17afc78aeb4653

1 in → 1 out8.5526 XPM116 B

AbwWkWZt…kawDhufa

8b35598353e74c…462f12665e621f

3 in → 1 out2.9900 XPM487 B

ASYDzXXq…MRQa5KvC

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.

2.016 × 10⁹⁸(99-digit number)

20164542275375111723…15263952348138214559

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

2.016 × 10⁹⁸(99-digit number)

20164542275375111723…15263952348138214559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.016 × 10⁹⁸(99-digit number)

20164542275375111723…15263952348138214561

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

4.032 × 10⁹⁸(99-digit number)

40329084550750223446…30527904696276429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.032 × 10⁹⁸(99-digit number)

40329084550750223446…30527904696276429121

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

8.065 × 10⁹⁸(99-digit number)

80658169101500446893…61055809392552858239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.065 × 10⁹⁸(99-digit number)

80658169101500446893…61055809392552858241

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

1.613 × 10⁹⁹(100-digit number)

16131633820300089378…22111618785105716479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.613 × 10⁹⁹(100-digit number)

16131633820300089378…22111618785105716481

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

3.226 × 10⁹⁹(100-digit number)

32263267640600178757…44223237570211432959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.226 × 10⁹⁹(100-digit number)

32263267640600178757…44223237570211432961

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