Block #3,048,941

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/11/2019, 10:34:10 PM · Difficulty 10.9961 · 3,794,394 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

969dbedb7615ddc6e9a73c415749345ee2c09659193aef312f39d714abc7909a

View on Chainz ↗

Height

#3,048,941

Difficulty

10.996087

Transactions

Size

1.14 KB

Version

Bits

0afeff8a

Nonce

871,106,601

Timestamp

2/11/2019, 10:34:10 PM

Confirmations

3,794,394

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

ff9e14cfa651c892a3e68e43e687a89170bb4068f61b743477260643af0af580

Transactions (2)

Coinbase24aa82732c5d1e…d8b4740c674dc1

1 in → 1 out8.2700 XPM110 B

AUhjokok…k5m93PZR

7529e952a09fd1…9d555440e2b5de

6 in → 2 out531.3000 XPM967 B

ARo9Bx54…mTopc3JB AGnNLYud…svAuz2gd

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.

1.660 × 10⁹²(93-digit number)

16609562164923840656…29979580101247588329

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

1.660 × 10⁹²(93-digit number)

16609562164923840656…29979580101247588329

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.660 × 10⁹²(93-digit number)

16609562164923840656…29979580101247588331

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

3.321 × 10⁹²(93-digit number)

33219124329847681313…59959160202495176659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.321 × 10⁹²(93-digit number)

33219124329847681313…59959160202495176661

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

6.643 × 10⁹²(93-digit number)

66438248659695362627…19918320404990353319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.643 × 10⁹²(93-digit number)

66438248659695362627…19918320404990353321

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

1.328 × 10⁹³(94-digit number)

13287649731939072525…39836640809980706639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.328 × 10⁹³(94-digit number)

13287649731939072525…39836640809980706641

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

2.657 × 10⁹³(94-digit number)

26575299463878145051…79673281619961413279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.657 × 10⁹³(94-digit number)

26575299463878145051…79673281619961413281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.315 × 10⁹³(94-digit number)

53150598927756290102…59346563239922826559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #3,048,941

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