Block #59,726

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 3:55:29 AM · Difficulty 8.9662 · 6,742,911 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d470c886c70f3ee5f76c253ab6fb432920054479806b5b1f8eb6e39b74dd4fd

View on Chainz ↗

Height

#59,726

Difficulty

8.966189

Transactions

Size

911 B

Version

Bits

08f75824

Nonce

Timestamp

7/18/2013, 3:55:29 AM

Confirmations

6,742,911

Mined by

⛏️ P2SHAeTcmmqHMYEKBSfvTp4dmwQ4JaLrFchfe1

Merkle Root

1571251e74764aaf4b60118d22a9f4ca32c164d4b7dc781b9a50e674f4befb53

Transactions (3)

Coinbase9245e9ceb98f2c…0766dd8a374e31

1 in → 1 out12.4400 XPM110 B

AeTcmmqH…LrFchfe1

14ee3e264fa939…779d5574a5cff6

3 in → 2 out64.1300 XPM487 B

AX7RRegM…phGr7fzS ANXc2j8A…iu9YNGc9

988e063540f52d…80c5529dec32fa

1 in → 2 out12.3300 XPM226 B

AbDkgyuG…pHPZu4yq APnpauHP…CbUxp126

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.

1.885 × 10⁹⁰(91-digit number)

18850947617747287596…65374602355011018159

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

1.885 × 10⁹⁰(91-digit number)

18850947617747287596…65374602355011018159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.885 × 10⁹⁰(91-digit number)

18850947617747287596…65374602355011018161

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

3.770 × 10⁹⁰(91-digit number)

37701895235494575192…30749204710022036319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.770 × 10⁹⁰(91-digit number)

37701895235494575192…30749204710022036321

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

7.540 × 10⁹⁰(91-digit number)

75403790470989150384…61498409420044072639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.540 × 10⁹⁰(91-digit number)

75403790470989150384…61498409420044072641

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

1.508 × 10⁹¹(92-digit number)

15080758094197830076…22996818840088145279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.508 × 10⁹¹(92-digit number)

15080758094197830076…22996818840088145281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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