Block #435,893

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 5:59:57 AM · Difficulty 10.3548 · 6,374,087 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

697cc1e2219b0bc4ec115b4990beb1b2964eb28f6e1d87173e0d847fcbf11277

View on Chainz ↗

Height

#435,893

Difficulty

10.354777

Transactions

Size

1.20 KB

Version

Bits

0a5ad2a9

Nonce

170,872

Timestamp

3/9/2014, 5:59:57 AM

Confirmations

6,374,087

Mined by

⛏️ aSSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9dc10a4b33a6078ac918f2f2651df8a48b84a3017531b6836f1e5371657087df

Transactions (2)

Coinbase6aa09baf53bd66…85be8b1f03c4af

1 in → 25 out9.3100 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

89a5bb97767f25…841a8f332b56f1

1 in → 2 out8375.6713 XPM226 B

AZopJ8Ka…Y4mwubyi AWPU2jTF…vbT6aBTN

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.

2.327 × 10⁹⁹(100-digit number)

23270949263808708167…56087356947658757119

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

2.327 × 10⁹⁹(100-digit number)

23270949263808708167…56087356947658757119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.327 × 10⁹⁹(100-digit number)

23270949263808708167…56087356947658757121

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

4.654 × 10⁹⁹(100-digit number)

46541898527617416334…12174713895317514239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.654 × 10⁹⁹(100-digit number)

46541898527617416334…12174713895317514241

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

9.308 × 10⁹⁹(100-digit number)

93083797055234832669…24349427790635028479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.308 × 10⁹⁹(100-digit number)

93083797055234832669…24349427790635028481

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

1.861 × 10¹⁰⁰(101-digit number)

18616759411046966533…48698855581270056959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.861 × 10¹⁰⁰(101-digit number)

18616759411046966533…48698855581270056961

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

3.723 × 10¹⁰⁰(101-digit number)

37233518822093933067…97397711162540113919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.723 × 10¹⁰⁰(101-digit number)

37233518822093933067…97397711162540113921

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 #435,893

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