Block #29,920

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 5:12:11 PM · Difficulty 7.9858 · 6,777,217 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3189e9e08e3bada608a0091ccfee445e7126b981592c05b5cc32018461f574a

View on Chainz ↗

Height

#29,920

Difficulty

7.985758

Transactions

Size

201 B

Version

Bits

07fc5a9e

Nonce

269

Timestamp

7/13/2013, 5:12:11 PM

Confirmations

6,777,217

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

9afc5f8e913bfeaebf1891e0ec536178422402b5ea14c3ef3638a49e8ff23cae

Transactions (1)

Coinbase9afc5f8e913bfe…38a49e8ff23cae

1 in → 1 out15.6600 XPM108 B

AGemJXng…w1K3MEut

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.

1.218 × 10¹⁰¹(102-digit number)

12189236743290747060…47145439115776716549

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

1.218 × 10¹⁰¹(102-digit number)

12189236743290747060…47145439115776716549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.218 × 10¹⁰¹(102-digit number)

12189236743290747060…47145439115776716551

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

2.437 × 10¹⁰¹(102-digit number)

24378473486581494120…94290878231553433099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.437 × 10¹⁰¹(102-digit number)

24378473486581494120…94290878231553433101

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

4.875 × 10¹⁰¹(102-digit number)

48756946973162988241…88581756463106866199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.875 × 10¹⁰¹(102-digit number)

48756946973162988241…88581756463106866201

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

9.751 × 10¹⁰¹(102-digit number)

97513893946325976482…77163512926213732399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.751 × 10¹⁰¹(102-digit number)

97513893946325976482…77163512926213732401

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

Block #29,920

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