Block #530,806

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/8/2014, 2:43:02 AM · Difficulty 10.8929 · 6,277,443 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

db7b4d61e4cfd188a5b15f2307a1249460051a9a3b154214b0be8f0fc7d1294b

View on Chainz ↗

Height

#530,806

Difficulty

10.892941

Transactions

Size

887 B

Version

Bits

0ae497c6

Nonce

117,861,140

Timestamp

5/8/2014, 2:43:02 AM

Confirmations

6,277,443

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d975c71bd76f061e16284fd0f97958d0580e96b71c95f7073dfdc103f7cbc039

Transactions (4)

Coinbase5cec516ada958e…6a7e712c6d8721

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

5dd76a2607a679…efdff1a1987306

1 in → 2 out6.3581 XPM226 B

AGdWVjRk…LFVsqCnK AKRFJmxh…EbQq9JGt

720a7d31f4a02e…b3c5e549bf41e5

1 in → 2 out4.8183 XPM225 B

AS9ZCvju…bu3NEFwZ ASt78ZkA…CMHVfEx9

56258e1146f2ee…65ffe4c4fa8c0f

1 in → 2 out4.8404 XPM227 B

AM6ndJPR…Y3STKwCc AG4jgfQm…4ssLmUJU

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.

8.869 × 10¹⁰⁰(101-digit number)

88697339040241451891…55217914408594631679

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

8.869 × 10¹⁰⁰(101-digit number)

88697339040241451891…55217914408594631679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.869 × 10¹⁰⁰(101-digit number)

88697339040241451891…55217914408594631681

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

1.773 × 10¹⁰¹(102-digit number)

17739467808048290378…10435828817189263359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.773 × 10¹⁰¹(102-digit number)

17739467808048290378…10435828817189263361

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

3.547 × 10¹⁰¹(102-digit number)

35478935616096580756…20871657634378526719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.547 × 10¹⁰¹(102-digit number)

35478935616096580756…20871657634378526721

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

7.095 × 10¹⁰¹(102-digit number)

70957871232193161513…41743315268757053439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.095 × 10¹⁰¹(102-digit number)

70957871232193161513…41743315268757053441

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

1.419 × 10¹⁰²(103-digit number)

14191574246438632302…83486630537514106879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.419 × 10¹⁰²(103-digit number)

14191574246438632302…83486630537514106881

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 #530,806

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