Block #1,617,792

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/7/2016, 10:42:49 AM · Difficulty 10.5856 · 5,224,735 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5eba6b1ee12da628bf1c56b74b0f86fae96221ef8c1abb74c02bf213ce1a3b1b

View on Chainz ↗

Height

#1,617,792

Difficulty

10.585611

Transactions

Size

1.14 KB

Version

Bits

0a95ea9b

Nonce

561,098,784

Timestamp

6/7/2016, 10:42:49 AM

Confirmations

5,224,735

Mined by

⛏️ P2SHAZjWiVVMu1gZKvnnZjDgqKU6MFCqcoijbP

Merkle Root

ef006fd41dfec14b5bc6c10284a00c844f17845de4bb4ee719d8fe06de57cb46

Transactions (2)

Coinbaseeb6f29071db710…b313d917ccb935

1 in → 1 out8.9300 XPM110 B

AZjWiVVM…CqcoijbP

982d69f87ded2c…914fa7ec80606e

6 in → 2 out455.0370 XPM965 B

AVd3vwsc…ZCM6bPmM AZ7xo3ni…aXTAFhZR

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.

1.087 × 10⁹⁷(98-digit number)

10879007451871869486…55277609408755240959

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

1.087 × 10⁹⁷(98-digit number)

10879007451871869486…55277609408755240959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.087 × 10⁹⁷(98-digit number)

10879007451871869486…55277609408755240961

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

2.175 × 10⁹⁷(98-digit number)

21758014903743738972…10555218817510481919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.175 × 10⁹⁷(98-digit number)

21758014903743738972…10555218817510481921

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

4.351 × 10⁹⁷(98-digit number)

43516029807487477945…21110437635020963839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.351 × 10⁹⁷(98-digit number)

43516029807487477945…21110437635020963841

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

8.703 × 10⁹⁷(98-digit number)

87032059614974955890…42220875270041927679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.703 × 10⁹⁷(98-digit number)

87032059614974955890…42220875270041927681

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

1.740 × 10⁹⁸(99-digit number)

17406411922994991178…84441750540083855359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.740 × 10⁹⁸(99-digit number)

17406411922994991178…84441750540083855361

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 #1,617,792

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