Block #2,132,834

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/26/2017, 2:03:27 AM · Difficulty 10.9101 · 4,710,163 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acfea7a273dfac46f93b3dbf74825f30ff26580bfa6c572023be7d60419b65fc

View on Chainz ↗

Height

#2,132,834

Difficulty

10.910122

Transactions

Size

427 B

Version

Bits

0ae8fdc3

Nonce

174,068,363

Timestamp

5/26/2017, 2:03:27 AM

Confirmations

4,710,163

Mined by

⛏️ P2SHAMpstRbfhzcRX3LJ22RT1E7h3NerXo32qr

Merkle Root

8972717a714d2ad7b41cf5deff3a466a8fbae4e7eb33938c4e02f4d901f7e6b0

Transactions (2)

Coinbase0736f1e416402f…5c91ae643dc46a

1 in → 1 out8.4000 XPM110 B

AMpstRbf…erXo32qr

485e8da93b7b7a…b6b7c6f0a06a69

1 in → 2 out9248.8349 XPM227 B

AW4PvqH4…sjozBgsb AV2FALkZ…xwSeEKGK

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.

8.480 × 10⁹³(94-digit number)

84806328223936566274…96613059291211642429

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

8.480 × 10⁹³(94-digit number)

84806328223936566274…96613059291211642429

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.480 × 10⁹³(94-digit number)

84806328223936566274…96613059291211642431

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

1.696 × 10⁹⁴(95-digit number)

16961265644787313254…93226118582423284859

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.696 × 10⁹⁴(95-digit number)

16961265644787313254…93226118582423284861

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

3.392 × 10⁹⁴(95-digit number)

33922531289574626509…86452237164846569719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.392 × 10⁹⁴(95-digit number)

33922531289574626509…86452237164846569721

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

6.784 × 10⁹⁴(95-digit number)

67845062579149253019…72904474329693139439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.784 × 10⁹⁴(95-digit number)

67845062579149253019…72904474329693139441

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

1.356 × 10⁹⁵(96-digit number)

13569012515829850603…45808948659386278879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.356 × 10⁹⁵(96-digit number)

13569012515829850603…45808948659386278881

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 #2,132,834

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