Block #2,903,747

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/31/2018, 12:38:28 AM · Difficulty 11.5732 · 3,929,790 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bfeb8b72141ce7ab23aba431e70819f5db3ff8962e04fe1959f2bff492d28854

View on Chainz ↗

Height

#2,903,747

Difficulty

11.573150

Transactions

Size

1.30 KB

Version

Bits

0b92b9fc

Nonce

963,814,888

Timestamp

10/31/2018, 12:38:28 AM

Confirmations

3,929,790

Mined by

⛏️ P2SHAZPgZRnCgR1TAWbWKbTj6bWJCydJd22prG

Merkle Root

a29f653ab8b526075d5037211d44e6dc9bc939999c5dad9261afb280dea389d5

Transactions (4)

Coinbase4a6b5c53d4a9a9…977c6409e4c3bc

1 in → 1 out7.4800 XPM110 B

AZPgZRnC…dJd22prG

f9eb89c8c85c24…c3da7ee239c124

2 in → 2 out14.8500 XPM306 B

AL7aWTBd…jn8ix1qY AKtg5M5J…UY3VCdzE

2ae55dac2be3c2…c83cb7957fc6da

2 in → 2 out14.8800 XPM306 B

AekJVbbR…3mPGtL7m AKfN5ELc…A3YNDXZ8

485cc1676ded6f…a48cd2d8a13879

3 in → 2 out10.2400 XPM520 B

ANEq6Gdi…Pbk4HtRv AcQqh4pM…3RCiiBGV

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.

1.456 × 10⁹⁸(99-digit number)

14562618081337323827…57689740587639767039

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

1.456 × 10⁹⁸(99-digit number)

14562618081337323827…57689740587639767039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.456 × 10⁹⁸(99-digit number)

14562618081337323827…57689740587639767041

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

2.912 × 10⁹⁸(99-digit number)

29125236162674647655…15379481175279534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.912 × 10⁹⁸(99-digit number)

29125236162674647655…15379481175279534081

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

5.825 × 10⁹⁸(99-digit number)

58250472325349295310…30758962350559068159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.825 × 10⁹⁸(99-digit number)

58250472325349295310…30758962350559068161

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

1.165 × 10⁹⁹(100-digit number)

11650094465069859062…61517924701118136319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.165 × 10⁹⁹(100-digit number)

11650094465069859062…61517924701118136321

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

2.330 × 10⁹⁹(100-digit number)

23300188930139718124…23035849402236272639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.330 × 10⁹⁹(100-digit number)

23300188930139718124…23035849402236272641

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

4.660 × 10⁹⁹(100-digit number)

46600377860279436248…46071698804472545279

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 #2,903,747

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