Block #29,112

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 2:25:09 PM · Difficulty 7.9838 · 6,781,004 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62955e33f516c3b0d83086717f8deb7c7ef01bcdc19ae65e7793cb058f724d1f

View on Chainz ↗

Height

#29,112

Difficulty

7.983801

Transactions

Size

202 B

Version

Bits

07fbda5c

Nonce

621

Timestamp

7/13/2013, 2:25:09 PM

Confirmations

6,781,004

Mined by

⛏️ P2SHAV3Mx3AqCBr85EUqewYnyDKYAdAKiwER2W

Merkle Root

0e96fd1151b41b066965efcf416171baaff6dc8d08a485444404e6dd82ec8a97

Transactions (1)

Coinbase0e96fd1151b41b…04e6dd82ec8a97

1 in → 1 out15.6700 XPM108 B

AV3Mx3Aq…AKiwER2W

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.

3.375 × 10¹⁰³(104-digit number)

33751528824303318731…89513165223563538199

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

3.375 × 10¹⁰³(104-digit number)

33751528824303318731…89513165223563538199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.375 × 10¹⁰³(104-digit number)

33751528824303318731…89513165223563538201

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

6.750 × 10¹⁰³(104-digit number)

67503057648606637462…79026330447127076399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.750 × 10¹⁰³(104-digit number)

67503057648606637462…79026330447127076401

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

1.350 × 10¹⁰⁴(105-digit number)

13500611529721327492…58052660894254152799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.350 × 10¹⁰⁴(105-digit number)

13500611529721327492…58052660894254152801

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

2.700 × 10¹⁰⁴(105-digit number)

27001223059442654984…16105321788508305599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 #29,112

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