Block #409,204

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 5:46:19 AM · Difficulty 10.4241 · 6,408,217 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d0235b3da7400b516cec6a68fc9bfbfaacee6d9d152b72234ce4651d95ac2f4

View on Chainz ↗

Height

#409,204

Difficulty

10.424120

Transactions

Size

1.13 KB

Version

Bits

0a6c931e

Nonce

6,368

Timestamp

2/18/2014, 5:46:19 AM

Confirmations

6,408,217

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

b15e7eb0fd941b942684ccb8f6f51fae173700411c7b7c2203b34dce5f7a7bac

Transactions (2)

Coinbase2678e51e4f18ef…6ae267d47e0a97

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

78fa98b1110ee4…41d0c974a14551

5 in → 9 out28.5417 XPM953 B

AQ85HiFh…1Tu9fuBM AJnuijiE…CxRBB9HV AZYLMbQF…gNR2dNnf ARLVb39P…bhtXdkU3 AKc9Rmjx…Bir3N5mm

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.

1.571 × 10¹⁰⁰(101-digit number)

15713937967626278659…22505892339179847679

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

1.571 × 10¹⁰⁰(101-digit number)

15713937967626278659…22505892339179847679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.571 × 10¹⁰⁰(101-digit number)

15713937967626278659…22505892339179847681

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

3.142 × 10¹⁰⁰(101-digit number)

31427875935252557319…45011784678359695359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.142 × 10¹⁰⁰(101-digit number)

31427875935252557319…45011784678359695361

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

6.285 × 10¹⁰⁰(101-digit number)

62855751870505114639…90023569356719390719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.285 × 10¹⁰⁰(101-digit number)

62855751870505114639…90023569356719390721

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

1.257 × 10¹⁰¹(102-digit number)

12571150374101022927…80047138713438781439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.257 × 10¹⁰¹(102-digit number)

12571150374101022927…80047138713438781441

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

2.514 × 10¹⁰¹(102-digit number)

25142300748202045855…60094277426877562879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.514 × 10¹⁰¹(102-digit number)

25142300748202045855…60094277426877562881

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 #409,204

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