Block #191,937

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 12:17:50 PM · Difficulty 9.8752 · 6,611,425 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5754abb50e87e146254a44538d432295451e00a89787c0e3caef88372e14fc4

View on Chainz ↗

Height

#191,937

Difficulty

9.875209

Transactions

Size

3.50 KB

Version

Bits

09e00db0

Nonce

1,164,805,531

Timestamp

10/3/2013, 12:17:50 PM

Confirmations

6,611,425

Mined by

⛏️ RM`=AaWbfbEjqTRU851D55bcrzKfQL2NnWBGLV

Merkle Root

4833bae10e331beebdce5fa0f0d17e5313d20c0ed99aee0cd35a383384c5864a

Transactions (1)

Coinbase4833bae10e331b…5a383384c5864a

1 in → 101 out10.2000 XPM3.41 KB

AaWbfbEj…2NnWBGLV AeLXg8qu…77XGoqwh AULkeUhX…SqqohfrX AewGmqcv…8ZoEhTt9 AY4DBdgz…6EoVAsfw

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.

1.276 × 10⁹⁴(95-digit number)

12762782850242247751…81392126343021860799

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

1.276 × 10⁹⁴(95-digit number)

12762782850242247751…81392126343021860799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.276 × 10⁹⁴(95-digit number)

12762782850242247751…81392126343021860801

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

2.552 × 10⁹⁴(95-digit number)

25525565700484495503…62784252686043721599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.552 × 10⁹⁴(95-digit number)

25525565700484495503…62784252686043721601

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

5.105 × 10⁹⁴(95-digit number)

51051131400968991006…25568505372087443199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.105 × 10⁹⁴(95-digit number)

51051131400968991006…25568505372087443201

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

1.021 × 10⁹⁵(96-digit number)

10210226280193798201…51137010744174886399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.021 × 10⁹⁵(96-digit number)

10210226280193798201…51137010744174886401

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

2.042 × 10⁹⁵(96-digit number)

20420452560387596402…02274021488349772799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.042 × 10⁹⁵(96-digit number)

20420452560387596402…02274021488349772801

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