Block #389,126

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 7:26:02 AM · Difficulty 10.4151 · 6,419,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b82712d0358db7674a8d00bed07d0b4ac2ad547eec5576b15a95390df9408510

View on Chainz ↗

Height

#389,126

Difficulty

10.415055

Transactions

Size

1.52 KB

Version

Bits

0a6a410a

Nonce

9,943

Timestamp

2/4/2014, 7:26:02 AM

Confirmations

6,419,873

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ec6973db36d733ed1180d17ab3164f8f7626e647d7447951bf8e38f397711e20

Transactions (2)

Coinbased50ef329f3b618…3e89892272726c

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

d4ffa140fb50f7…46ab4250b58058

7 in → 13 out37.4053 XPM1.32 KB

AJSUWQXb…Q2uQtCdp AXHHDSVj…SvbeMuQi AeKNrjNj…1NEq95Ta AS791b91…2oFChkDv AMqYHLJu…5Pij3cMm

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.

5.524 × 10⁹⁹(100-digit number)

55246178720847042188…04303954133085061119

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

5.524 × 10⁹⁹(100-digit number)

55246178720847042188…04303954133085061119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.524 × 10⁹⁹(100-digit number)

55246178720847042188…04303954133085061121

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

1.104 × 10¹⁰⁰(101-digit number)

11049235744169408437…08607908266170122239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.104 × 10¹⁰⁰(101-digit number)

11049235744169408437…08607908266170122241

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

2.209 × 10¹⁰⁰(101-digit number)

22098471488338816875…17215816532340244479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.209 × 10¹⁰⁰(101-digit number)

22098471488338816875…17215816532340244481

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

4.419 × 10¹⁰⁰(101-digit number)

44196942976677633750…34431633064680488959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.419 × 10¹⁰⁰(101-digit number)

44196942976677633750…34431633064680488961

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

8.839 × 10¹⁰⁰(101-digit number)

88393885953355267501…68863266129360977919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.839 × 10¹⁰⁰(101-digit number)

88393885953355267501…68863266129360977921

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 #389,126

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