Block #290,726

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 8:10:17 PM · Difficulty 9.9894 · 6,517,242 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0cdb4744d4b7a50e94803417e296440af686cb07ee1d3b0ebbb743f2f02014bb

View on Chainz ↗

Height

#290,726

Difficulty

9.989410

Transactions

Size

1.11 KB

Version

Bits

09fd49f2

Nonce

79,874

Timestamp

12/2/2013, 8:10:17 PM

Confirmations

6,517,242

Mined by

⛏️ oaRaAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

5281816e49d2f9a96a3dbf909a4062bc60c5690e34bd98f03fd18abe6ad897d4

Transactions (1)

Coinbase5281816e49d2f9…d18abe6ad897d4

1 in → 29 out9.9900 XPM1.02 KB

AZninDSu…FvgDMwC4 AdimvR9u…9e7MP6ui AToTBTPr…X3DsBU1U ATMigTP7…hXB68JA2 AKEwr54i…9BfmMkRh

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.

2.731 × 10⁹⁰(91-digit number)

27310172339424380109…18837959503877950399

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

2.731 × 10⁹⁰(91-digit number)

27310172339424380109…18837959503877950399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.731 × 10⁹⁰(91-digit number)

27310172339424380109…18837959503877950401

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

5.462 × 10⁹⁰(91-digit number)

54620344678848760218…37675919007755900799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.462 × 10⁹⁰(91-digit number)

54620344678848760218…37675919007755900801

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

1.092 × 10⁹¹(92-digit number)

10924068935769752043…75351838015511801599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.092 × 10⁹¹(92-digit number)

10924068935769752043…75351838015511801601

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

2.184 × 10⁹¹(92-digit number)

21848137871539504087…50703676031023603199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.184 × 10⁹¹(92-digit number)

21848137871539504087…50703676031023603201

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

4.369 × 10⁹¹(92-digit number)

43696275743079008174…01407352062047206399

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 #290,726

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