Block #2,922,577

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/14/2018, 11:43:35 AM · Difficulty 11.3667 · 3,919,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4488c65dc56159b9fd571d009f941814b6449e657519e13d065e9ca91f856ee9

View on Chainz ↗

Height

#2,922,577

Difficulty

11.366671

Transactions

Size

1.16 KB

Version

Bits

0b5dde20

Nonce

2,136,060,108

Timestamp

11/14/2018, 11:43:35 AM

Confirmations

3,919,552

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

4bfa23a431b0a5bba586d112b3034708be847691c3fb73c2463fa4b5ba25abe7

Transactions (4)

Coinbasecf1dde4669c03f…47a7455bc1e877

1 in → 1 out7.7600 XPM110 B

AbXwmGxD…4XXYP765

edc2a8b52c0d81…0c41a55f46e8fd

2 in → 2 out15.4900 XPM307 B

AZW9Zv5x…mVPYfgfr AFx6oJsh…xGvAjqU5

9560626436afca…856dd857f40e36

2 in → 2 out15.3700 XPM306 B

ATyjvTXU…scaPtq81 AJCs4NTV…BjV4Ljfh

b71d2cb90e2059…da317ad1e3a8eb

2 in → 2 out10.8500 XPM374 B

AJq3UFQA…m73xvHtY APVKWthF…PMMxwRoz

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.

1.191 × 10⁹⁶(97-digit number)

11919328402185109051…24065245018262755839

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

1.191 × 10⁹⁶(97-digit number)

11919328402185109051…24065245018262755839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.191 × 10⁹⁶(97-digit number)

11919328402185109051…24065245018262755841

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

2.383 × 10⁹⁶(97-digit number)

23838656804370218103…48130490036525511679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.383 × 10⁹⁶(97-digit number)

23838656804370218103…48130490036525511681

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

4.767 × 10⁹⁶(97-digit number)

47677313608740436206…96260980073051023359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.767 × 10⁹⁶(97-digit number)

47677313608740436206…96260980073051023361

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

9.535 × 10⁹⁶(97-digit number)

95354627217480872412…92521960146102046719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.535 × 10⁹⁶(97-digit number)

95354627217480872412…92521960146102046721

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

1.907 × 10⁹⁷(98-digit number)

19070925443496174482…85043920292204093439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.907 × 10⁹⁷(98-digit number)

19070925443496174482…85043920292204093441

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

3.814 × 10⁹⁷(98-digit number)

38141850886992348964…70087840584408186879

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 #2,922,577

Cookie Preferences