Block #2,159,731

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/14/2017, 1:27:46 AM · Difficulty 10.9029 · 4,665,560 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94f45206f851cb3dac6f7fdf21e053993f392e67bfd4688a8f59ca5b5d246ea7

View on Chainz ↗

Height

#2,159,731

Difficulty

10.902921

Transactions

Size

6.13 KB

Version

Bits

0ae725d9

Nonce

1,565,390,613

Timestamp

6/14/2017, 1:27:46 AM

Confirmations

4,665,560

Mined by

⛏️ P2SHAFnuPC1SQEN3RAAccNWAC7D2qfaRiuHuix

Merkle Root

b5320b878b1428c14db61f164abfe1c0ed3fc44a2463cbb4ea32b1483ad77cdd

Transactions (3)

Coinbase7c338bffe683e3…26e383e44f44ab

1 in → 1 out8.4800 XPM110 B

AFnuPC1S…aRiuHuix

e673437ec0500f…968527ee9367ec

30 in → 1 out959.9900 XPM4.37 KB

AcxhUhX6…N8N8w2tm

7aca3f3d87041a…d0efb7dc6675d2

13 in → 2 out104.3600 XPM1.56 KB

AVcZwfqK…V7r6aAoc ASsDdXSL…ERAy6ybe

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.

9.036 × 10⁹⁴(95-digit number)

90369979396066408002…15321944333562487359

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

9.036 × 10⁹⁴(95-digit number)

90369979396066408002…15321944333562487359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.036 × 10⁹⁴(95-digit number)

90369979396066408002…15321944333562487361

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

1.807 × 10⁹⁵(96-digit number)

18073995879213281600…30643888667124974719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.807 × 10⁹⁵(96-digit number)

18073995879213281600…30643888667124974721

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

3.614 × 10⁹⁵(96-digit number)

36147991758426563200…61287777334249949439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.614 × 10⁹⁵(96-digit number)

36147991758426563200…61287777334249949441

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

7.229 × 10⁹⁵(96-digit number)

72295983516853126401…22575554668499898879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.229 × 10⁹⁵(96-digit number)

72295983516853126401…22575554668499898881

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

1.445 × 10⁹⁶(97-digit number)

14459196703370625280…45151109336999797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.445 × 10⁹⁶(97-digit number)

14459196703370625280…45151109336999797761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,159,731

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