Block #2,257,750

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/18/2017, 8:18:37 PM · Difficulty 10.9520 · 4,583,430 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c3247cae567cc24e03fe887fe22d5db39bc011dfd2ce90e07ae0f2dbf8f65fe9

View on Chainz ↗

Height

#2,257,750

Difficulty

10.951995

Transactions

Size

573 B

Version

Bits

0af3b5ed

Nonce

191,225,593

Timestamp

8/18/2017, 8:18:37 PM

Confirmations

4,583,430

Mined by

⛏️ P2SHAUFqgx65GroWga33CHAMabBfHqewqNpZXh

Merkle Root

986d57f9ada62d4973733800b9a95509164d91c6f8d096e8b932d4cebcede790

Transactions (2)

Coinbase5180d6efd5a678…5080df50940acb

1 in → 1 out8.3300 XPM110 B

AUFqgx65…ewqNpZXh

977e4079ce3822…f787a14eaa764f

2 in → 2 out4.0250 XPM374 B

AZwEKUDj…TCExVfgH Ad2L4SF1…SPQYYWiv

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.

1.230 × 10⁹³(94-digit number)

12306414306647810632…37256513318196386559

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

1.230 × 10⁹³(94-digit number)

12306414306647810632…37256513318196386559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.230 × 10⁹³(94-digit number)

12306414306647810632…37256513318196386561

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

2.461 × 10⁹³(94-digit number)

24612828613295621265…74513026636392773119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.461 × 10⁹³(94-digit number)

24612828613295621265…74513026636392773121

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

4.922 × 10⁹³(94-digit number)

49225657226591242531…49026053272785546239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.922 × 10⁹³(94-digit number)

49225657226591242531…49026053272785546241

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

9.845 × 10⁹³(94-digit number)

98451314453182485063…98052106545571092479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.845 × 10⁹³(94-digit number)

98451314453182485063…98052106545571092481

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

1.969 × 10⁹⁴(95-digit number)

19690262890636497012…96104213091142184959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.969 × 10⁹⁴(95-digit number)

19690262890636497012…96104213091142184961

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

3.938 × 10⁹⁴(95-digit number)

39380525781272994025…92208426182284369919

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

Block #2,257,750

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