Block #195,614

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 10:48:15 PM · Difficulty 9.8799 · 6,614,318 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c11ce70e8c2711096472fdd760ca50231bb59d5d4bc16b5ddd8b65f1c8511cd

View on Chainz ↗

Height

#195,614

Difficulty

9.879934

Transactions

Size

1.12 KB

Version

Bits

09e14361

Nonce

68,565

Timestamp

10/5/2013, 10:48:15 PM

Confirmations

6,614,318

Mined by

⛏️ P2SHAGr3vkkouSvBxV1fV9WWEYnVosUwqcfU8R

Merkle Root

7d4936a525eb2a7cdae6d6c5df1f470cef0c3c38adea5d39ce05e2893f3a0e02

Transactions (4)

Coinbase5374f874a5f68c…3827a9eba975ec

1 in → 1 out10.2600 XPM109 B

AGr3vkko…UwqcfU8R

34102236bd9af4…950cec258844df

1 in → 1 out10.3000 XPM158 B

ASNHbKyk…FYmTuopD

d7c4116ed4165d…8c36cd5959fc40

1 in → 1 out71.9179 XPM192 B

AN8EsDuh…eeBAeeho

7af08e49d44bcd…4258289bc8a01e

4 in → 2 out21.0149 XPM601 B

AJaVHUgD…4e6RkzzX AP2EXyfx…TjZP8f5n

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.

7.104 × 10⁹⁴(95-digit number)

71049586675976937069…75419040101494024279

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

7.104 × 10⁹⁴(95-digit number)

71049586675976937069…75419040101494024279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.104 × 10⁹⁴(95-digit number)

71049586675976937069…75419040101494024281

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

1.420 × 10⁹⁵(96-digit number)

14209917335195387413…50838080202988048559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.420 × 10⁹⁵(96-digit number)

14209917335195387413…50838080202988048561

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

2.841 × 10⁹⁵(96-digit number)

28419834670390774827…01676160405976097119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.841 × 10⁹⁵(96-digit number)

28419834670390774827…01676160405976097121

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

5.683 × 10⁹⁵(96-digit number)

56839669340781549655…03352320811952194239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.683 × 10⁹⁵(96-digit number)

56839669340781549655…03352320811952194241

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

1.136 × 10⁹⁶(97-digit number)

11367933868156309931…06704641623904388479

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 #195,614

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