Block #77,781

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 1:21:04 PM · Difficulty 9.1970 · 6,729,085 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8dcb854be8524deae1c7022a87f8a72dadd22ab1e8edd32b29ab46874794976

View on Chainz ↗

Height

#77,781

Difficulty

9.197003

Transactions

Size

857 B

Version

Bits

09326ed2

Nonce

308

Timestamp

7/22/2013, 1:21:04 PM

Confirmations

6,729,085

Mined by

⛏️ P2SHALhMfwM3C1rByXizupTcHCc1HEaSBijzDt

Merkle Root

4669d6625b67cef08fb2a862df0ae7d0dcc36f918dd18673e87a672c7419741c

Transactions (3)

Coinbase0e5e02b9ea6482…3c93af8f1d73e9

1 in → 1 out11.8300 XPM110 B

ALhMfwM3…aSBijzDt

3983ddd797dcf3…0a86ef071840af

1 in → 2 out109.9465 XPM227 B

ATZd6KSe…ACGPt7PT AUkSNxRK…cy291qHR

bfc034cbafe106…b8bf3e0912c4ec

3 in → 2 out37.0600 XPM420 B

AMgPY6TK…RXnkSo4M AbpNTEnb…ExW9cBcP

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.

2.019 × 10¹¹⁹(120-digit number)

20197169804029687487…83080702752768361319

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

2.019 × 10¹¹⁹(120-digit number)

20197169804029687487…83080702752768361319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.019 × 10¹¹⁹(120-digit number)

20197169804029687487…83080702752768361321

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

4.039 × 10¹¹⁹(120-digit number)

40394339608059374974…66161405505536722639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.039 × 10¹¹⁹(120-digit number)

40394339608059374974…66161405505536722641

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

8.078 × 10¹¹⁹(120-digit number)

80788679216118749949…32322811011073445279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.078 × 10¹¹⁹(120-digit number)

80788679216118749949…32322811011073445281

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

1.615 × 10¹²⁰(121-digit number)

16157735843223749989…64645622022146890559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.615 × 10¹²⁰(121-digit number)

16157735843223749989…64645622022146890561

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

3.231 × 10¹²⁰(121-digit number)

32315471686447499979…29291244044293781119

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

Block #77,781

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