Block #138,203

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/28/2013, 6:56:36 AM · Difficulty 9.8246 · 6,688,193 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2592355d54a77036132d5062c19284be38e5d56d9c5f619ebaa13ec06be83428

View on Chainz ↗

Height

#138,203

Difficulty

9.824559

Transactions

Size

1.22 KB

Version

Bits

09d3164a

Nonce

58,500

Timestamp

8/28/2013, 6:56:36 AM

Confirmations

6,688,193

Mined by

⛏️ P2SHAWPh3V4bLAUTpZrnMtPLg7AJBJSbWA19so

Merkle Root

88c1b1dc500f80049d64bd1e7eb1859c13cfb949da9edd380a2d63cff8b03ff5

Transactions (5)

Coinbasef76e398dc9dcd5…12c7ce3210fe80

1 in → 1 out10.3800 XPM109 B

AWPh3V4b…SbWA19so

c7f448dd0ece1c…36ca04373d7768

2 in → 2 out387.3206 XPM373 B

AGqAQ6Ht…RspmpBWC APRiwdTY…zLpYVpjT

edad3e098a0ff4…86bd387d0d22ef

1 in → 2 out10.3700 XPM227 B

Ad5ostL6…Zi963SR1 AbvPGdpW…nARb1BE3

372582029dbafb…9bf83f91840dac

1 in → 2 out8.3084 XPM227 B

AQkCXVaL…iN1GB5D2 ALnYVXgj…RyGa1dRe

a3b1bef9d31621…0a06b1571b1e97

1 in → 2 out3.6787 XPM226 B

AcBSBiM5…9Sv4yVet ARC6rYoT…iPU3BTuN

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.

9.143 × 10⁹⁶(97-digit number)

91435993489104662144…67057898830154271719

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

9.143 × 10⁹⁶(97-digit number)

91435993489104662144…67057898830154271719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.143 × 10⁹⁶(97-digit number)

91435993489104662144…67057898830154271721

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

1.828 × 10⁹⁷(98-digit number)

18287198697820932428…34115797660308543439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.828 × 10⁹⁷(98-digit number)

18287198697820932428…34115797660308543441

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

3.657 × 10⁹⁷(98-digit number)

36574397395641864857…68231595320617086879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.657 × 10⁹⁷(98-digit number)

36574397395641864857…68231595320617086881

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

7.314 × 10⁹⁷(98-digit number)

73148794791283729715…36463190641234173759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.314 × 10⁹⁷(98-digit number)

73148794791283729715…36463190641234173761

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

1.462 × 10⁹⁸(99-digit number)

14629758958256745943…72926381282468347519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #138,203

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