Block #1,135,617

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/1/2015, 11:28:01 AM · Difficulty 10.9405 · 5,680,975 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b1151d92825b8444181fbf476060f61e406ac31ef03fa775af8ee468deba8f8

View on Chainz ↗

Height

#1,135,617

Difficulty

10.940453

Transactions

Size

10.82 KB

Version

Bits

0af0c188

Nonce

1,006,289,120

Timestamp

7/1/2015, 11:28:01 AM

Confirmations

5,680,975

Mined by

⛏️ P2SHAKoje9aGYQKa4JCPSh8TZwCfhmdKDd7vfJ

Merkle Root

04cad545c4a5a88a7528ad8571c82d598afaf60effc477cc58dc981f4035fb24

Transactions (2)

Coinbasee973444674e579…f1215a7c72bfa8

1 in → 1 out8.4600 XPM110 B

AKoje9aG…dKDd7vfJ

1484b25ce9392f…8a9e4aab8c83ec

73 in → 2 out500.0100 XPM10.62 KB

AJjnK9uC…VreFquR4 AL7PSTpK…2bCZEVnu

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.

7.097 × 10⁹²(93-digit number)

70970496668604494573…52959807399917013119

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

7.097 × 10⁹²(93-digit number)

70970496668604494573…52959807399917013119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.097 × 10⁹²(93-digit number)

70970496668604494573…52959807399917013121

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

1.419 × 10⁹³(94-digit number)

14194099333720898914…05919614799834026239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.419 × 10⁹³(94-digit number)

14194099333720898914…05919614799834026241

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

2.838 × 10⁹³(94-digit number)

28388198667441797829…11839229599668052479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.838 × 10⁹³(94-digit number)

28388198667441797829…11839229599668052481

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

5.677 × 10⁹³(94-digit number)

56776397334883595658…23678459199336104959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.677 × 10⁹³(94-digit number)

56776397334883595658…23678459199336104961

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

1.135 × 10⁹⁴(95-digit number)

11355279466976719131…47356918398672209919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.135 × 10⁹⁴(95-digit number)

11355279466976719131…47356918398672209921

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 #1,135,617

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