Block #59,729

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 3:57:19 AM · Difficulty 8.9662 · 6,739,086 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

33f1cbfb96ae4c7cefe313efe511a8dfa8438242a0008b5ca0a53181b688430f

View on Chainz ↗

Height

#59,729

Difficulty

8.966201

Transactions

Size

569 B

Version

Bits

08f758ed

Nonce

Timestamp

7/18/2013, 3:57:19 AM

Confirmations

6,739,086

Mined by

⛏️ P2SHAKCeEpi5bkpub5ACftX6GKMoojABjP77dd

Merkle Root

954a9457e5a262e52a461500b975180ed1096714fa02e84de2e547a1104d710b

Transactions (2)

Coinbase35cc79273e71c0…a3394ce8c73a21

1 in → 1 out12.4300 XPM110 B

AKCeEpi5…ABjP77dd

8cff1872d9d81f…11739b553e5ec9

2 in → 2 out108.8600 XPM373 B

AQnNKxxD…xyvGpsKY AaU3yEYr…w8AJttbc

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.

1.232 × 10⁸⁵(86-digit number)

12321107129525966992…80797905455919035919

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

1.232 × 10⁸⁵(86-digit number)

12321107129525966992…80797905455919035919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.232 × 10⁸⁵(86-digit number)

12321107129525966992…80797905455919035921

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

2.464 × 10⁸⁵(86-digit number)

24642214259051933985…61595810911838071839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.464 × 10⁸⁵(86-digit number)

24642214259051933985…61595810911838071841

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

4.928 × 10⁸⁵(86-digit number)

49284428518103867971…23191621823676143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.928 × 10⁸⁵(86-digit number)

49284428518103867971…23191621823676143681

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

9.856 × 10⁸⁵(86-digit number)

98568857036207735943…46383243647352287359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.856 × 10⁸⁵(86-digit number)

98568857036207735943…46383243647352287361

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

1.971 × 10⁸⁶(87-digit number)

19713771407241547188…92766487294704574719

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