Block #2,178,193

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/25/2017, 11:42:58 PM · Difficulty 10.9253 · 4,659,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

916b12f66fec1effc0c9facfaa35dc1148fd0b78dc63758c5760cb6a517e4fc0

View on Chainz ↗

Height

#2,178,193

Difficulty

10.925257

Transactions

Size

756 B

Version

Bits

0aecdda5

Nonce

163,023,466

Timestamp

6/25/2017, 11:42:58 PM

Confirmations

4,659,385

Mined by

⛏️ P2SHAWfE4g7iHsi1XkFpozE947ZAX5qisJdc9r

Merkle Root

ee6cf152eb947d32740244491839b89b40feecdeb40ee05ddfbd8d875fd88ac9

Transactions (2)

Coinbased42564e1fd75df…9f5dbb40d1ef77

1 in → 1 out8.3700 XPM110 B

AWfE4g7i…qisJdc9r

89314769223206…5409e5a07c1ec1

3 in → 3 out5311.0716 XPM556 B

Ac2WPyVJ…pTZzzXcP AVYB63sx…VuuEo8f5 AHKEqLWG…Z6JsKv41

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.

4.466 × 10⁹³(94-digit number)

44662279379865498467…81879907561395260869

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

4.466 × 10⁹³(94-digit number)

44662279379865498467…81879907561395260869

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.466 × 10⁹³(94-digit number)

44662279379865498467…81879907561395260871

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

8.932 × 10⁹³(94-digit number)

89324558759730996934…63759815122790521739

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.932 × 10⁹³(94-digit number)

89324558759730996934…63759815122790521741

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

1.786 × 10⁹⁴(95-digit number)

17864911751946199386…27519630245581043479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.786 × 10⁹⁴(95-digit number)

17864911751946199386…27519630245581043481

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

3.572 × 10⁹⁴(95-digit number)

35729823503892398773…55039260491162086959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.572 × 10⁹⁴(95-digit number)

35729823503892398773…55039260491162086961

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

7.145 × 10⁹⁴(95-digit number)

71459647007784797547…10078520982324173919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.145 × 10⁹⁴(95-digit number)

71459647007784797547…10078520982324173921

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

1.429 × 10⁹⁵(96-digit number)

14291929401556959509…20157041964648347839

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 #2,178,193

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