Block #192,310

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/3/2013, 6:43:26 PM · Difficulty 9.8749 · 6,603,154 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c293e9c384964d247b4559bdf4c40c0ba43084d698a5f1b022460d87c5433716

View on Chainz ↗

Height

#192,310

Difficulty

9.874906

Transactions

Size

4.72 KB

Version

Bits

09dff9d2

Nonce

1,164,880,906

Timestamp

10/3/2013, 6:43:26 PM

Confirmations

6,603,154

Mined by

⛏️ 6RM5AXEf9r4aNJr16hy3j2Mf1Dahbc54V7EYi4

Merkle Root

362eb007136b32e3359716bead81c6aef76b583632ef788b7e2e445ca0a186ac

Transactions (2)

Coinbase7bf186d26b4b5d…e320905f4c34e1

1 in → 112 out10.2100 XPM3.78 KB

AXEf9r4a…54V7EYi4 Ac7qBAbo…VB3ybHpP AYpuBdQC…4rn5bQ8b APtCCTjk…etXBZujq AS5X2XNw…NKGEK3GT

cb74862060d1c9…568adc994ed7a3

7 in → 1 out62.5800 XPM875 B

AZDw8GgW…GexTkqVt

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.

1.427 × 10⁹⁵(96-digit number)

14276873507879816994…37087332703117542899

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

1.427 × 10⁹⁵(96-digit number)

14276873507879816994…37087332703117542899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.427 × 10⁹⁵(96-digit number)

14276873507879816994…37087332703117542901

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

2.855 × 10⁹⁵(96-digit number)

28553747015759633988…74174665406235085799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.855 × 10⁹⁵(96-digit number)

28553747015759633988…74174665406235085801

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

5.710 × 10⁹⁵(96-digit number)

57107494031519267977…48349330812470171599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.710 × 10⁹⁵(96-digit number)

57107494031519267977…48349330812470171601

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

1.142 × 10⁹⁶(97-digit number)

11421498806303853595…96698661624940343199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.142 × 10⁹⁶(97-digit number)

11421498806303853595…96698661624940343201

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

2.284 × 10⁹⁶(97-digit number)

22842997612607707191…93397323249880686399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.284 × 10⁹⁶(97-digit number)

22842997612607707191…93397323249880686401

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.568 × 10⁹⁶(97-digit number)

45685995225215414382…86794646499761372799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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