Block #483,966

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 8:02:29 AM · Difficulty 10.5746 · 6,342,619 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6b4a866132c51ce62ab3d3c594db64b5485114dd3ef1ae6605951b3c41857cd

View on Chainz ↗

Height

#483,966

Difficulty

10.574556

Transactions

Size

1.22 KB

Version

Bits

0a931613

Nonce

245,779,218

Timestamp

4/10/2014, 8:02:29 AM

Confirmations

6,342,619

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

411e694bc30563933b818ea435db468d10a99c8e2071be550bcc92d70cea3abd

Transactions (3)

Coinbase518c7b3c3bad0c…b08a87f561ae03

1 in → 1 out8.9500 XPM116 B

AbwWkWZt…kawDhufa

6a73678cc3bc65…523297abdbfaae

2 in → 2 out6.3178 XPM373 B

AVsjqzCG…L9hN77hn AFqiv3bg…uxYjxX9f

d567a491ec5201…5a65a4c1f1a350

4 in → 2 out5.0623 XPM672 B

AajNJWSe…BA9SUyyq AMU8nEj9…Eo32pqxr

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.

7.388 × 10⁹⁷(98-digit number)

73884954384642916121…57765056213150106559

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

7.388 × 10⁹⁷(98-digit number)

73884954384642916121…57765056213150106559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.388 × 10⁹⁷(98-digit number)

73884954384642916121…57765056213150106561

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

1.477 × 10⁹⁸(99-digit number)

14776990876928583224…15530112426300213119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.477 × 10⁹⁸(99-digit number)

14776990876928583224…15530112426300213121

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

2.955 × 10⁹⁸(99-digit number)

29553981753857166448…31060224852600426239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.955 × 10⁹⁸(99-digit number)

29553981753857166448…31060224852600426241

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

5.910 × 10⁹⁸(99-digit number)

59107963507714332897…62120449705200852479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.910 × 10⁹⁸(99-digit number)

59107963507714332897…62120449705200852481

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

1.182 × 10⁹⁹(100-digit number)

11821592701542866579…24240899410401704959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.182 × 10⁹⁹(100-digit number)

11821592701542866579…24240899410401704961

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 #483,966

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