Block #3,049,194

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/12/2019, 2:51:00 AM · Difficulty 10.9961 · 3,790,896 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd43f718ae6268d4ba176b8faf20e9fe3b30dd199037f7ab07df544ae144f8fd

View on Chainz ↗

Height

#3,049,194

Difficulty

10.996091

Transactions

Size

4.03 KB

Version

Bits

0afeffd8

Nonce

1,549,401,752

Timestamp

2/12/2019, 2:51:00 AM

Confirmations

3,790,896

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

4b591cc3f192bea6b6cbcdf581b83ac07c0d9f4001264c7d3eac06f4c6809e84

Transactions (2)

Coinbasee6d557993ef8ba…9e2996b59ffdf9

1 in → 1 out8.3000 XPM110 B

AUMQRepm…tAfKmdW1

397530118ea816…33fe3a238823c1

26 in → 2 out4000.0100 XPM3.83 KB

AMiDURXf…CyGdgR4c AUWLiCGG…uTwceacQ

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.

1.362 × 10⁹⁵(96-digit number)

13624072379682291614…05489524985796219899

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

1.362 × 10⁹⁵(96-digit number)

13624072379682291614…05489524985796219899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.362 × 10⁹⁵(96-digit number)

13624072379682291614…05489524985796219901

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

2.724 × 10⁹⁵(96-digit number)

27248144759364583229…10979049971592439799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.724 × 10⁹⁵(96-digit number)

27248144759364583229…10979049971592439801

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

5.449 × 10⁹⁵(96-digit number)

54496289518729166458…21958099943184879599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.449 × 10⁹⁵(96-digit number)

54496289518729166458…21958099943184879601

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

1.089 × 10⁹⁶(97-digit number)

10899257903745833291…43916199886369759199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.089 × 10⁹⁶(97-digit number)

10899257903745833291…43916199886369759201

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

2.179 × 10⁹⁶(97-digit number)

21798515807491666583…87832399772739518399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.179 × 10⁹⁶(97-digit number)

21798515807491666583…87832399772739518401

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 #3,049,194

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