Block #292,203

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 2:44:02 PM · Difficulty 9.9902 · 6,522,939 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

540d2aa1c0423a261e31248025712b94fea07a3e92cfcba34b8d3c54087d8a2e

View on Chainz ↗

Height

#292,203

Difficulty

9.990191

Transactions

Size

1.11 KB

Version

Bits

09fd7d2a

Nonce

47,279

Timestamp

12/3/2013, 2:44:02 PM

Confirmations

6,522,939

Mined by

⛏️ kuaR.AZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

c7cb8a3e6c7e6c91bd957cad3cc16e276de962ea32a1238fef259c9f808d3621

Transactions (1)

Coinbasec7cb8a3e6c7e6c…259c9f808d3621

1 in → 29 out9.9800 XPM1.02 KB

AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz AVaz6eMX…TCAgqi1U AbQmpRKY…QqaAZabm AKKBh74a…WUkS6XH2

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.

3.827 × 10⁹⁵(96-digit number)

38274436970750808374…55065653495911554239

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

3.827 × 10⁹⁵(96-digit number)

38274436970750808374…55065653495911554239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.827 × 10⁹⁵(96-digit number)

38274436970750808374…55065653495911554241

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

7.654 × 10⁹⁵(96-digit number)

76548873941501616748…10131306991823108479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.654 × 10⁹⁵(96-digit number)

76548873941501616748…10131306991823108481

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

1.530 × 10⁹⁶(97-digit number)

15309774788300323349…20262613983646216959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.530 × 10⁹⁶(97-digit number)

15309774788300323349…20262613983646216961

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

3.061 × 10⁹⁶(97-digit number)

30619549576600646699…40525227967292433919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.061 × 10⁹⁶(97-digit number)

30619549576600646699…40525227967292433921

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

6.123 × 10⁹⁶(97-digit number)

61239099153201293398…81050455934584867839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.123 × 10⁹⁶(97-digit number)

61239099153201293398…81050455934584867841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #292,203

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