Block #293,935

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 2:35:00 PM · Difficulty 9.9908 · 6,515,211 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21a8a129ff530d492eaf02e0d517411f5f57c9dc4aa29da87cb1db6d0eb85003

View on Chainz ↗

Height

#293,935

Difficulty

9.990816

Transactions

Size

1.18 KB

Version

Bits

09fda621

Nonce

291,614

Timestamp

12/4/2013, 2:35:00 PM

Confirmations

6,515,211

Mined by

⛏️ |aR=lARcqMJhpYZE2kngc2mc4PFnwnaRVLToQ6S

Merkle Root

5a29a742e02bbf6c3d2dd52bb31f2b4540b79607ae8bd54ae9f87e914c9a9af5

Transactions (1)

Coinbase5a29a742e02bbf…f87e914c9a9af5

1 in → 31 out9.9800 XPM1.09 KB

ARcqMJhp…RVLToQ6S AcM3ext6…Hwtj9Qp3 ASXEwJrb…E3MLWChF AYcLTeXR…bscgPops ATr7rJvZ…v4W3ybba

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.

9.662 × 10⁹⁴(95-digit number)

96629972790752613945…42999840458094589439

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

9.662 × 10⁹⁴(95-digit number)

96629972790752613945…42999840458094589439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.662 × 10⁹⁴(95-digit number)

96629972790752613945…42999840458094589441

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

1.932 × 10⁹⁵(96-digit number)

19325994558150522789…85999680916189178879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.932 × 10⁹⁵(96-digit number)

19325994558150522789…85999680916189178881

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

3.865 × 10⁹⁵(96-digit number)

38651989116301045578…71999361832378357759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.865 × 10⁹⁵(96-digit number)

38651989116301045578…71999361832378357761

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

7.730 × 10⁹⁵(96-digit number)

77303978232602091156…43998723664756715519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.730 × 10⁹⁵(96-digit number)

77303978232602091156…43998723664756715521

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

1.546 × 10⁹⁶(97-digit number)

15460795646520418231…87997447329513431039

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 #293,935

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