Block #2,235,968

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/4/2017, 2:18:51 AM · Difficulty 10.9458 · 4,607,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c543f574693e926f3eaf87121c39284afed1a41dc8b3a8c43ac9c690b512155

View on Chainz ↗

Height

#2,235,968

Difficulty

10.945846

Transactions

Size

2.64 KB

Version

Bits

0af222f7

Nonce

1,056,978,217

Timestamp

8/4/2017, 2:18:51 AM

Confirmations

4,607,655

Mined by

⛏️ P2SHAYfdDBTfkKMBs2Mhr6v88ZVm3xvxMPfz4s

Merkle Root

4359204322588416e7b199732b0c73389a0cd23c05570fb640f20bae049a9304

Transactions (3)

Coinbase09bf1baf167bbf…db7bc294017663

1 in → 1 out8.3700 XPM110 B

AYfdDBTf…vxMPfz4s

c84d5cf88cb040…66190944c25b9e

6 in → 1 out24.0000 XPM865 B

ARezZb4y…FxP7ivbi

a9a90a82fd74de…f42f5312b52c63

11 in → 2 out20.0300 XPM1.60 KB

AG3yMnVp…7zjjypic AS51EuJK…Pny1AN5r

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.

7.425 × 10⁹¹(92-digit number)

74253556051368644193…29178671653887793919

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

7.425 × 10⁹¹(92-digit number)

74253556051368644193…29178671653887793919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.425 × 10⁹¹(92-digit number)

74253556051368644193…29178671653887793921

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

1.485 × 10⁹²(93-digit number)

14850711210273728838…58357343307775587839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.485 × 10⁹²(93-digit number)

14850711210273728838…58357343307775587841

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

2.970 × 10⁹²(93-digit number)

29701422420547457677…16714686615551175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.970 × 10⁹²(93-digit number)

29701422420547457677…16714686615551175681

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

5.940 × 10⁹²(93-digit number)

59402844841094915354…33429373231102351359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.940 × 10⁹²(93-digit number)

59402844841094915354…33429373231102351361

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

1.188 × 10⁹³(94-digit number)

11880568968218983070…66858746462204702719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.188 × 10⁹³(94-digit number)

11880568968218983070…66858746462204702721

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 #2,235,968

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