Block #194,984

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 11:59:07 AM · Difficulty 9.8803 · 6,612,383 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70a158114beb87fcbcc3063258e0eb1e5edab7f921211c464f64b1615a7c8267

View on Chainz ↗

Height

#194,984

Difficulty

9.880277

Transactions

Size

4.10 KB

Version

Bits

09e159d0

Nonce

1,164,762,831

Timestamp

10/5/2013, 11:59:07 AM

Confirmations

6,612,383

Mined by

⛏️ ROAP7ZfMBNshaRzuTbGCP8TGZbe6n8aVFt5X

Merkle Root

a26378d524569cb57aa1eb665a8d19538f2d1e323f42ac6ed5a12bbf1dd4b12d

Transactions (1)

Coinbasea26378d524569c…a12bbf1dd4b12d

1 in → 119 out10.1800 XPM4.01 KB

AP7ZfMBN…n8aVFt5X AUXba14R…Fdfwmv6D AebfwVBz…ZtQwaXb8 ALiqMFRk…RZhDAqsV AWVGtkZj…m321bzSA

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.

3.702 × 10⁸⁹(90-digit number)

37021265478511471172…03199396930201740309

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

3.702 × 10⁸⁹(90-digit number)

37021265478511471172…03199396930201740309

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.702 × 10⁸⁹(90-digit number)

37021265478511471172…03199396930201740311

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

7.404 × 10⁸⁹(90-digit number)

74042530957022942345…06398793860403480619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.404 × 10⁸⁹(90-digit number)

74042530957022942345…06398793860403480621

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

1.480 × 10⁹⁰(91-digit number)

14808506191404588469…12797587720806961239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.480 × 10⁹⁰(91-digit number)

14808506191404588469…12797587720806961241

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

2.961 × 10⁹⁰(91-digit number)

29617012382809176938…25595175441613922479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.961 × 10⁹⁰(91-digit number)

29617012382809176938…25595175441613922481

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

5.923 × 10⁹⁰(91-digit number)

59234024765618353876…51190350883227844959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.923 × 10⁹⁰(91-digit number)

59234024765618353876…51190350883227844961

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 #194,984

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