Block #94,814

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/3/2013, 8:06:26 AM · Difficulty 9.2088 · 6,701,330 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

31a575a22689adfcaefdcb455db7f902c9915049a8607b8316aaf975c434ed0a

View on Chainz ↗

Height

#94,814

Difficulty

9.208787

Transactions

Size

1.14 KB

Version

Bits

0935730a

Nonce

8,293

Timestamp

8/3/2013, 8:06:26 AM

Confirmations

6,701,330

Mined by

⛏️ P2SHAPfYjGW2iXGVaFTMTj2uZivX1S5C1RgJmz

Merkle Root

5b3d475dd9d4129c85141b726678d381cdb9738354baa2709ce585d20d9f3c06

Transactions (2)

Coinbase9b1a8067a993fa…062247d65e2283

1 in → 1 out11.7900 XPM109 B

APfYjGW2…5C1RgJmz

a72536c15b8a7f…073a6c59568500

6 in → 2 out45.0103 XPM963 B

AcWxiJYv…LPH1Kib5 ASader9k…Zug3a59W

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.

5.359 × 10¹⁰⁸(109-digit number)

53598112688482127434…92137094900067748629

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

5.359 × 10¹⁰⁸(109-digit number)

53598112688482127434…92137094900067748629

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.359 × 10¹⁰⁸(109-digit number)

53598112688482127434…92137094900067748631

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

1.071 × 10¹⁰⁹(110-digit number)

10719622537696425486…84274189800135497259

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.071 × 10¹⁰⁹(110-digit number)

10719622537696425486…84274189800135497261

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

2.143 × 10¹⁰⁹(110-digit number)

21439245075392850973…68548379600270994519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.143 × 10¹⁰⁹(110-digit number)

21439245075392850973…68548379600270994521

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

4.287 × 10¹⁰⁹(110-digit number)

42878490150785701947…37096759200541989039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.287 × 10¹⁰⁹(110-digit number)

42878490150785701947…37096759200541989041

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

8.575 × 10¹⁰⁹(110-digit number)

85756980301571403895…74193518401083978079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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