Block #1,761,658

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/13/2016, 7:19:30 PM · Difficulty 10.7385 · 5,080,740 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9b6c0b40cee9642d7a5df4f85fd558be506e7d2f9912b26169b6a7e400116dc

View on Chainz ↗

Height

#1,761,658

Difficulty

10.738452

Transactions

Size

1.39 KB

Version

Bits

0abd0b2f

Nonce

2,001,481,044

Timestamp

9/13/2016, 7:19:30 PM

Confirmations

5,080,740

Mined by

⛏️ P2SHAcobx6ci5ij6JVTFCMEv2N44KQVHdYyKVd

Merkle Root

f4f79799ef4ff4ce86e5d9dbee4612cab31ae6237e9d24884838943d984f5ce7

Transactions (2)

Coinbase9529253a516339…9ea50c7c1561b5

1 in → 1 out8.6800 XPM109 B

Acobx6ci…VHdYyKVd

6555cdea5f46f3…ff0771680e808f

8 in → 1 out0.1887 XPM1.20 KB

AUKV3Goi…ajcvvDKN

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.

1.086 × 10⁹³(94-digit number)

10861993808969227768…54401652594151893359

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

1.086 × 10⁹³(94-digit number)

10861993808969227768…54401652594151893359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.086 × 10⁹³(94-digit number)

10861993808969227768…54401652594151893361

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

2.172 × 10⁹³(94-digit number)

21723987617938455536…08803305188303786719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.172 × 10⁹³(94-digit number)

21723987617938455536…08803305188303786721

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

4.344 × 10⁹³(94-digit number)

43447975235876911073…17606610376607573439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.344 × 10⁹³(94-digit number)

43447975235876911073…17606610376607573441

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

8.689 × 10⁹³(94-digit number)

86895950471753822147…35213220753215146879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.689 × 10⁹³(94-digit number)

86895950471753822147…35213220753215146881

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

1.737 × 10⁹⁴(95-digit number)

17379190094350764429…70426441506430293759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.737 × 10⁹⁴(95-digit number)

17379190094350764429…70426441506430293761

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 #1,761,658

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