Block #139,244

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/28/2013, 9:19:18 PM · Difficulty 9.8307 · 6,670,061 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5cca350782faf518bae9371dca2a1ca27aa843b6851822b3ab400aacd6d3dadf

View on Chainz ↗

Height

#139,244

Difficulty

9.830715

Transactions

Size

428 B

Version

Bits

09d4a9b8

Nonce

29,918

Timestamp

8/28/2013, 9:19:18 PM

Confirmations

6,670,061

Mined by

⛏️ P2SHALsWNY8YQbPiDcGt7oFfYegKoiENk7NgeG

Merkle Root

77053ddbb3f984fe6b468e7272fbc0fcff6096015a30b68a75edbacfb8265185

Transactions (2)

Coinbaseb34211b70c669d…1b175ffb4f3e8f

1 in → 1 out10.3400 XPM109 B

ALsWNY8Y…ENk7NgeG

979a37fe8d1457…bc804bf8b9bca7

1 in → 2 out6.2791 XPM226 B

ATuWxsBa…dKFZ3gRq AbNrnavE…uozLC85k

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.

1.143 × 10¹⁰¹(102-digit number)

11433398212404070065…17811557912596165519

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

1.143 × 10¹⁰¹(102-digit number)

11433398212404070065…17811557912596165519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.143 × 10¹⁰¹(102-digit number)

11433398212404070065…17811557912596165521

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

2.286 × 10¹⁰¹(102-digit number)

22866796424808140131…35623115825192331039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.286 × 10¹⁰¹(102-digit number)

22866796424808140131…35623115825192331041

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

4.573 × 10¹⁰¹(102-digit number)

45733592849616280262…71246231650384662079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.573 × 10¹⁰¹(102-digit number)

45733592849616280262…71246231650384662081

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

9.146 × 10¹⁰¹(102-digit number)

91467185699232560524…42492463300769324159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.146 × 10¹⁰¹(102-digit number)

91467185699232560524…42492463300769324161

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

1.829 × 10¹⁰²(103-digit number)

18293437139846512104…84984926601538648319

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 #139,244

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