Block #292,154

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 2:12:12 PM · Difficulty 9.9902 · 6,517,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cd00c763356947f7be5ffec7495a1b20bc6a4ff64e6b244ee498625e64926710

View on Chainz ↗

Height

#292,154

Difficulty

9.990161

Transactions

Size

1.03 KB

Version

Bits

09fd7b37

Nonce

54,948

Timestamp

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

Confirmations

6,517,757

Mined by

⛏️ :uaREAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

83db06897e3219476a02dd55dd2c04e66232e23dd4902ed66f869c1fed384336

Transactions (2)

Coinbase36187685dd1153…e2a18b750f3fec

1 in → 20 out10.0000 XPM743 B

AZninDSu…FvgDMwC4 AKde1i4d…88R1bw6g APeshfYV…3PKcKMKH AHUtCSic…9RMQggzJ AWm233nS…1dJSnVJJ

911815c68eb74f…8db81d21ea7208

1 in → 2 out20542.6586 XPM225 B

AVFaNkVj…9cHtV5nf AZWjEt9J…cGkL7vrJ

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.

1.392 × 10⁹³(94-digit number)

13929366406497948645…10169110685441029119

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

1.392 × 10⁹³(94-digit number)

13929366406497948645…10169110685441029119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.392 × 10⁹³(94-digit number)

13929366406497948645…10169110685441029121

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

2.785 × 10⁹³(94-digit number)

27858732812995897290…20338221370882058239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.785 × 10⁹³(94-digit number)

27858732812995897290…20338221370882058241

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

5.571 × 10⁹³(94-digit number)

55717465625991794581…40676442741764116479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.571 × 10⁹³(94-digit number)

55717465625991794581…40676442741764116481

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

1.114 × 10⁹⁴(95-digit number)

11143493125198358916…81352885483528232959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.114 × 10⁹⁴(95-digit number)

11143493125198358916…81352885483528232961

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

2.228 × 10⁹⁴(95-digit number)

22286986250396717832…62705770967056465919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.228 × 10⁹⁴(95-digit number)

22286986250396717832…62705770967056465921

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 #292,154

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