Block #562,976

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/26/2014, 3:29:49 PM · Difficulty 10.9647 · 6,246,479 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be8ca2edac314d0743001c4d690042ee0235a2eba05c24c458e03a1f2787684c

View on Chainz ↗

Height

#562,976

Difficulty

10.964693

Transactions

Size

1.41 KB

Version

Bits

0af6f627

Nonce

6,714,612

Timestamp

5/26/2014, 3:29:49 PM

Confirmations

6,246,479

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4859a25a3470154c71cdf7f47d027f7fd569018c70c70cd67ea1cfd0b2cde953

Transactions (4)

Coinbase741784a605d99c…d4f3b8dde3c260

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

0469ef44811d09…736291c9d6ce40

2 in → 2 out7.8150 XPM374 B

AXBkGbmH…XLRqweeD APgLECvA…Pksbf42R

23ad0aa65ce0a0…416690a810d96a

4 in → 1 out2.0021 XPM634 B

AS8suiHE…ZYgV8fig

b1631606773973…37069fca2e2c10

1 in → 2 out5.5881 XPM227 B

AGriVrzg…oREzYqvR Ac1EfC5U…bJX8pZTT

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.

1.869 × 10⁹⁸(99-digit number)

18693064387997227792…83182139586380167999

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

1.869 × 10⁹⁸(99-digit number)

18693064387997227792…83182139586380167999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.869 × 10⁹⁸(99-digit number)

18693064387997227792…83182139586380168001

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

3.738 × 10⁹⁸(99-digit number)

37386128775994455585…66364279172760335999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.738 × 10⁹⁸(99-digit number)

37386128775994455585…66364279172760336001

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

7.477 × 10⁹⁸(99-digit number)

74772257551988911170…32728558345520671999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.477 × 10⁹⁸(99-digit number)

74772257551988911170…32728558345520672001

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

1.495 × 10⁹⁹(100-digit number)

14954451510397782234…65457116691041343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.495 × 10⁹⁹(100-digit number)

14954451510397782234…65457116691041344001

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

2.990 × 10⁹⁹(100-digit number)

29908903020795564468…30914233382082687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.990 × 10⁹⁹(100-digit number)

29908903020795564468…30914233382082688001

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 #562,976

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