Block #3,000,772

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/8/2019, 1:26:06 PM · Difficulty 11.2151 · 3,825,820 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74acd71bfcfa20122f8ea4c868c34ad8797557bab73ea7be894886e6abeb8c69

View on Chainz ↗

Height

#3,000,772

Difficulty

11.215072

Transactions

Size

1018 B

Version

Bits

0b370ef9

Nonce

579,081,578

Timestamp

1/8/2019, 1:26:06 PM

Confirmations

3,825,820

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

bf4ba6e774ffdb7913865a7bf286d5e3b46c82a36800586ed9d086ba5dc855a6

Transactions (2)

Coinbaseec4903b0ee4c21…50a42d8759341a

1 in → 1 out7.9500 XPM109 B

AUhjokok…k5m93PZR

9bb449d459fc77…eb7db5890eeaba

5 in → 2 out332.6667 XPM818 B

AeoYRFM9…akPhgXp7 AcMBCYEu…fNV4GaxP

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.

2.264 × 10⁹⁶(97-digit number)

22640251150874114783…91712091879593390719

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

2.264 × 10⁹⁶(97-digit number)

22640251150874114783…91712091879593390719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.264 × 10⁹⁶(97-digit number)

22640251150874114783…91712091879593390721

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

4.528 × 10⁹⁶(97-digit number)

45280502301748229566…83424183759186781439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.528 × 10⁹⁶(97-digit number)

45280502301748229566…83424183759186781441

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

9.056 × 10⁹⁶(97-digit number)

90561004603496459132…66848367518373562879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.056 × 10⁹⁶(97-digit number)

90561004603496459132…66848367518373562881

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

1.811 × 10⁹⁷(98-digit number)

18112200920699291826…33696735036747125759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.811 × 10⁹⁷(98-digit number)

18112200920699291826…33696735036747125761

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

3.622 × 10⁹⁷(98-digit number)

36224401841398583653…67393470073494251519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.622 × 10⁹⁷(98-digit number)

36224401841398583653…67393470073494251521

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

7.244 × 10⁹⁷(98-digit number)

72448803682797167306…34786940146988503039

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 #3,000,772

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