Block #506,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 5:17:09 AM · Difficulty 10.8141 · 6,297,124 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b806f11ea1070ae5c0ac52ae6c0ae674d2bcfb8ce4a69e1a157c8a0f88538e0

View on Chainz ↗

Height

#506,622

Difficulty

10.814074

Transactions

Size

1.47 KB

Version

Bits

0ad0672e

Nonce

182,406,208

Timestamp

4/23/2014, 5:17:09 AM

Confirmations

6,297,124

Mined by

⛏️ P2SHAKZ6yRCRGSbs3PS5FTeH3541YuGoQTXUc5

Merkle Root

1a745387fca274d7822ad6e5ac418a0fbc250a1b51d3439031526ca4d6499d46

Transactions (4)

Coinbase7cc3a10ae53260…383cc1add1c263

1 in → 1 out8.5700 XPM111 B

AKZ6yRCR…GoQTXUc5

c57580d9993f21…b4e0fbf5b9054a

4 in → 2 out124.4472 XPM671 B

AdQWstqz…SfBeWNHr AGdoF52d…WQVENWG7

e8488823c63a74…19643081844fe3

2 in → 5 out17.0900 XPM407 B

AbzQpH8m…uhgc6kzg AGw7KuTT…ZfJmwhoB AeKNrjNj…1NEq95Ta AXbbkuVv…UixHY7hn AFrDzxcC…UjLgWneU

1ea589fd30b3c4…a7913b006c7b26

1 in → 2 out2.2811 XPM226 B

AH4q5MUm…4HcTdUWB AVn7rePr…KdiirF9W

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.

2.101 × 10⁹⁸(99-digit number)

21012641165745324896…48197909972556079999

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

2.101 × 10⁹⁸(99-digit number)

21012641165745324896…48197909972556079999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.101 × 10⁹⁸(99-digit number)

21012641165745324896…48197909972556080001

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

4.202 × 10⁹⁸(99-digit number)

42025282331490649792…96395819945112159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.202 × 10⁹⁸(99-digit number)

42025282331490649792…96395819945112160001

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

8.405 × 10⁹⁸(99-digit number)

84050564662981299585…92791639890224319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.405 × 10⁹⁸(99-digit number)

84050564662981299585…92791639890224320001

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

1.681 × 10⁹⁹(100-digit number)

16810112932596259917…85583279780448639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.681 × 10⁹⁹(100-digit number)

16810112932596259917…85583279780448640001

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

3.362 × 10⁹⁹(100-digit number)

33620225865192519834…71166559560897279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.362 × 10⁹⁹(100-digit number)

33620225865192519834…71166559560897280001

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