Block #2,471,737

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/13/2018, 10:27:25 PM · Difficulty 10.9622 · 4,371,944 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3fa8ffe7a48c52b709d4faefdd42729246f0e4bf6cd3f5909ea18d2b4c484c76

View on Chainz ↗

Height

#2,471,737

Difficulty

10.962233

Transactions

Size

846 B

Version

Bits

0af654e2

Nonce

365,622,805

Timestamp

1/13/2018, 10:27:25 PM

Confirmations

4,371,944

Mined by

⛏️ P2SHAJwHS22yX2piyE725kru2yYSaBsQZWP1bw

Merkle Root

4869cac517682d6b2b29e045465d046cbd2a408f008fe3dbf9be864609bc2c70

Transactions (4)

Coinbase2d4ebd87d28dd1…6da3bd29f03e67

1 in → 1 out8.3400 XPM110 B

AJwHS22y…sQZWP1bw

223336c1dca864…4347af88911036

1 in → 2 out8.3000 XPM192 B

AaUjgbny…KoYqKQYU AJgjP9ZD…YQr5uLBn

9845764221e57f…b4afe01a6b2ae8

1 in → 2 out6.5949 XPM227 B

ANxNfXmZ…4p5PaHCM AN256zvN…Gungod7w

9b12140efa0a43…62eac58d037d62

1 in → 2 out4.2133 XPM226 B

AX93RTy7…8Mb2JW1U AMjZ87GH…cvurqAXE

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.

3.159 × 10⁹⁷(98-digit number)

31597391591802900644…44306280342819143679

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

3.159 × 10⁹⁷(98-digit number)

31597391591802900644…44306280342819143679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.159 × 10⁹⁷(98-digit number)

31597391591802900644…44306280342819143681

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

6.319 × 10⁹⁷(98-digit number)

63194783183605801288…88612560685638287359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.319 × 10⁹⁷(98-digit number)

63194783183605801288…88612560685638287361

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

1.263 × 10⁹⁸(99-digit number)

12638956636721160257…77225121371276574719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.263 × 10⁹⁸(99-digit number)

12638956636721160257…77225121371276574721

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

2.527 × 10⁹⁸(99-digit number)

25277913273442320515…54450242742553149439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.527 × 10⁹⁸(99-digit number)

25277913273442320515…54450242742553149441

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

5.055 × 10⁹⁸(99-digit number)

50555826546884641030…08900485485106298879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.055 × 10⁹⁸(99-digit number)

50555826546884641030…08900485485106298881

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

1.011 × 10⁹⁹(100-digit number)

10111165309376928206…17800970970212597759

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 #2,471,737

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