Block #2,649,519

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/5/2018, 7:28:00 AM · Difficulty 11.7640 · 4,183,467 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdf4a25be0783e51f7fd24039f1cc63f904fc4396dd94ba2194e59d020071012

View on Chainz ↗

Height

#2,649,519

Difficulty

11.763984

Transactions

Size

428 B

Version

Bits

0bc39471

Nonce

1,995,077,295

Timestamp

5/5/2018, 7:28:00 AM

Confirmations

4,183,467

Mined by

⛏️ P2SHAXsTVFBq5W9Hu3EZHBhN9gtsmX5XSfgZNY

Merkle Root

4e47196de5d207b2ab56235de9c73b40a5636764c322b5a9f3b27b1b798ff852

Transactions (2)

Coinbase89624a0105de42…fe0bb40edce4d8

1 in → 1 out7.2200 XPM110 B

AXsTVFBq…5XSfgZNY

a0f4d99d2a1171…83c40567c81da8

1 in → 2 out1866.3025 XPM227 B

AGGn6SJu…QVxKbSrU ALZ9p3Jj…Nc8qTRsf

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.

7.038 × 10⁹⁶(97-digit number)

70386998727304205296…44565201424543866879

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

7.038 × 10⁹⁶(97-digit number)

70386998727304205296…44565201424543866879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.038 × 10⁹⁶(97-digit number)

70386998727304205296…44565201424543866881

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

1.407 × 10⁹⁷(98-digit number)

14077399745460841059…89130402849087733759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.407 × 10⁹⁷(98-digit number)

14077399745460841059…89130402849087733761

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

2.815 × 10⁹⁷(98-digit number)

28154799490921682118…78260805698175467519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.815 × 10⁹⁷(98-digit number)

28154799490921682118…78260805698175467521

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

5.630 × 10⁹⁷(98-digit number)

56309598981843364237…56521611396350935039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.630 × 10⁹⁷(98-digit number)

56309598981843364237…56521611396350935041

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

1.126 × 10⁹⁸(99-digit number)

11261919796368672847…13043222792701870079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.126 × 10⁹⁸(99-digit number)

11261919796368672847…13043222792701870081

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

2.252 × 10⁹⁸(99-digit number)

22523839592737345694…26086445585403740159

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 #2,649,519

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