Block #486,332

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/11/2014, 1:07:03 PM · Difficulty 10.6243 · 6,327,494 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8286700d68d027cca631662ad9a43d7561fd6d877262c7ed2b06d462e12f9152

View on Chainz ↗

Height

#486,332

Difficulty

10.624259

Transactions

Size

15.88 KB

Version

Bits

0a9fcf6c

Nonce

9,472

Timestamp

4/11/2014, 1:07:03 PM

Confirmations

6,327,494

Mined by

⛏️ P2SHAcRQ6RG392SquanLBy6NW5pBxzCJXqzzWn

Merkle Root

e084199f155372b22eccc550a6b8cc1102e10d0f149ccdd4eda32e0400ffea20

Transactions (2)

Coinbase0e7a53e3261136…23ff515babd422

1 in → 1 out9.0200 XPM112 B

AcRQ6RG3…CJXqzzWn

3f5fc55d784876…6efe9367d635e0

108 in → 2 out500.0100 XPM15.69 KB

AJjnK9uC…VreFquR4 ATAvSFqG…4h1bKYrd

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.

9.914 × 10⁹⁵(96-digit number)

99148714593181603724…38071951179794027399

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

9.914 × 10⁹⁵(96-digit number)

99148714593181603724…38071951179794027399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.914 × 10⁹⁵(96-digit number)

99148714593181603724…38071951179794027401

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

1.982 × 10⁹⁶(97-digit number)

19829742918636320744…76143902359588054799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.982 × 10⁹⁶(97-digit number)

19829742918636320744…76143902359588054801

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

3.965 × 10⁹⁶(97-digit number)

39659485837272641489…52287804719176109599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.965 × 10⁹⁶(97-digit number)

39659485837272641489…52287804719176109601

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

7.931 × 10⁹⁶(97-digit number)

79318971674545282979…04575609438352219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.931 × 10⁹⁶(97-digit number)

79318971674545282979…04575609438352219201

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

1.586 × 10⁹⁷(98-digit number)

15863794334909056595…09151218876704438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.586 × 10⁹⁷(98-digit number)

15863794334909056595…09151218876704438401

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 #486,332

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