Block #193,928

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 7:51:54 PM · Difficulty 9.8778 · 6,616,898 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e5ceaae43fb2f62fcc7eb542f66ac6c229353195e26778e0f6b36f379d79399b

View on Chainz ↗

Height

#193,928

Difficulty

9.877794

Transactions

Size

3.63 KB

Version

Bits

09e0b718

Nonce

1,164,948,333

Timestamp

10/4/2013, 7:51:54 PM

Confirmations

6,616,898

Mined by

⛏️ RO*AKeDh1uSCtaDWEBCHXEXx7BNs6Th9Hwfjg

Merkle Root

606894b64e8eed1b915fc73dcc1cf1cd958ffe80a304ee357b338ad90158b53b

Transactions (1)

Coinbase606894b64e8eed…338ad90158b53b

1 in → 105 out10.1900 XPM3.55 KB

AKeDh1uS…Th9Hwfjg AVU5ekRm…jGkw6Fsz AcS2hSgb…TQfHx7Ra ATeGzPEb…fEYhKxfs AUR9p73Y…fRttwfyn

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.

1.155 × 10⁹⁴(95-digit number)

11558950305224952237…16850264092397196399

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

1.155 × 10⁹⁴(95-digit number)

11558950305224952237…16850264092397196399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.155 × 10⁹⁴(95-digit number)

11558950305224952237…16850264092397196401

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

2.311 × 10⁹⁴(95-digit number)

23117900610449904474…33700528184794392799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.311 × 10⁹⁴(95-digit number)

23117900610449904474…33700528184794392801

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

4.623 × 10⁹⁴(95-digit number)

46235801220899808948…67401056369588785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.623 × 10⁹⁴(95-digit number)

46235801220899808948…67401056369588785601

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

9.247 × 10⁹⁴(95-digit number)

92471602441799617897…34802112739177571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.247 × 10⁹⁴(95-digit number)

92471602441799617897…34802112739177571201

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

1.849 × 10⁹⁵(96-digit number)

18494320488359923579…69604225478355142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.849 × 10⁹⁵(96-digit number)

18494320488359923579…69604225478355142401

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 #193,928

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