Block #478,282

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 11:48:26 PM · Difficulty 10.4917 · 6,348,708 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff846ddc97a2066c98b69e7d010abe2944c9e952a793e519dd98bb7c4c56c1ca

View on Chainz ↗

Height

#478,282

Difficulty

10.491749

Transactions

Size

725 B

Version

Bits

0a7de340

Nonce

24,955

Timestamp

4/6/2014, 11:48:26 PM

Confirmations

6,348,708

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

a9fa5c24128063d3b4f9072a4faa1a5a0581cdd782ffb0808abe3f76b0fdb2c4

Transactions (2)

Coinbase3272340950c54d…762da22982baf5

1 in → 1 out9.0800 XPM110 B

AeKNrjNj…1NEq95Ta

8b66981ef224d8…7166866eb46715

3 in → 2 out35.0103 XPM522 B

AQJc6a92…8JisnJ7F AUBtTt78…6xYjFg4m

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.

3.338 × 10¹⁰²(103-digit number)

33385366140981651082…03045353579718021119

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

3.338 × 10¹⁰²(103-digit number)

33385366140981651082…03045353579718021119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.338 × 10¹⁰²(103-digit number)

33385366140981651082…03045353579718021121

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

6.677 × 10¹⁰²(103-digit number)

66770732281963302165…06090707159436042239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.677 × 10¹⁰²(103-digit number)

66770732281963302165…06090707159436042241

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

1.335 × 10¹⁰³(104-digit number)

13354146456392660433…12181414318872084479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.335 × 10¹⁰³(104-digit number)

13354146456392660433…12181414318872084481

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

2.670 × 10¹⁰³(104-digit number)

26708292912785320866…24362828637744168959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.670 × 10¹⁰³(104-digit number)

26708292912785320866…24362828637744168961

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

5.341 × 10¹⁰³(104-digit number)

53416585825570641732…48725657275488337919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.341 × 10¹⁰³(104-digit number)

53416585825570641732…48725657275488337921

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 #478,282

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