Block #409,227

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 6:09:41 AM · Difficulty 10.4243 · 6,401,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

226d5bfc58d6f9db847d9d2284d509064846cfad315c7dca2bbf7c4f08eb6975

View on Chainz ↗

Height

#409,227

Difficulty

10.424322

Transactions

Size

587 B

Version

Bits

0a6ca066

Nonce

439

Timestamp

2/18/2014, 6:09:41 AM

Confirmations

6,401,046

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6ca378d66261231636436e49716639b3f27750c22cdb02d87eb4c9281e512735

Transactions (2)

Coinbase48259a6e09bda9…f0febe86d1fd52

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

bea7f1f2b4c55c…aec02240175c48

2 in → 2 out1.9927 XPM375 B

ATv5Pf8k…XbBgTGiY AMggKrEB…SkeHdPKW

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.

4.608 × 10¹⁰⁹(110-digit number)

46089864861839251167…87196219577047449599

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

4.608 × 10¹⁰⁹(110-digit number)

46089864861839251167…87196219577047449599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.608 × 10¹⁰⁹(110-digit number)

46089864861839251167…87196219577047449601

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

9.217 × 10¹⁰⁹(110-digit number)

92179729723678502334…74392439154094899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.217 × 10¹⁰⁹(110-digit number)

92179729723678502334…74392439154094899201

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

1.843 × 10¹¹⁰(111-digit number)

18435945944735700466…48784878308189798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.843 × 10¹¹⁰(111-digit number)

18435945944735700466…48784878308189798401

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

3.687 × 10¹¹⁰(111-digit number)

36871891889471400933…97569756616379596799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.687 × 10¹¹⁰(111-digit number)

36871891889471400933…97569756616379596801

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

7.374 × 10¹¹⁰(111-digit number)

73743783778942801867…95139513232759193599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.374 × 10¹¹⁰(111-digit number)

73743783778942801867…95139513232759193601

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 #409,227

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