Block #270,443

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 11:00:18 PM · Difficulty 9.9517 · 6,536,304 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4e059a1fe7e76550d50008817b73160428953e11df476f7684ca04bc91bfd3f3

View on Chainz ↗

Height

#270,443

Difficulty

9.951724

Transactions

Size

2.11 KB

Version

Bits

09f3a42a

Nonce

200,259

Timestamp

11/23/2013, 11:00:18 PM

Confirmations

6,536,304

Mined by

⛏️ kAKFMENK8Y83ntTmGeVC63vAJZ8b6knxLfH

Merkle Root

4b1520c91396e9f13dcf43a93fe46660001ab46e6286353612df130419f01dc5

Transactions (1)

Coinbase4b1520c91396e9…df130419f01dc5

1 in → 59 out10.0500 XPM2.02 KB

AKFMENK8…b6knxLfH AcRG9vnh…TuQSD8LP AHTTUHKB…g8V7VRLq ANHbaxZp…XjnHCJJs AP2GxFDi…MZQBdSYt

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.

1.019 × 10⁹³(94-digit number)

10195990401092274456…51172828571659878399

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

1.019 × 10⁹³(94-digit number)

10195990401092274456…51172828571659878399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.019 × 10⁹³(94-digit number)

10195990401092274456…51172828571659878401

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

2.039 × 10⁹³(94-digit number)

20391980802184548913…02345657143319756799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.039 × 10⁹³(94-digit number)

20391980802184548913…02345657143319756801

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

4.078 × 10⁹³(94-digit number)

40783961604369097827…04691314286639513599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.078 × 10⁹³(94-digit number)

40783961604369097827…04691314286639513601

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

8.156 × 10⁹³(94-digit number)

81567923208738195654…09382628573279027199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.156 × 10⁹³(94-digit number)

81567923208738195654…09382628573279027201

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

1.631 × 10⁹⁴(95-digit number)

16313584641747639130…18765257146558054399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.631 × 10⁹⁴(95-digit number)

16313584641747639130…18765257146558054401

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 #270,443

Cookie Preferences