Block #1,314,779

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/6/2015, 1:05:47 AM · Difficulty 10.8605 · 5,530,091 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3fc46e05e62391f593d23ab9a45158efb61a08f68933882afea8739ba934de15

View on Chainz ↗

Height

#1,314,779

Difficulty

10.860452

Transactions

Size

733 B

Version

Bits

0adc469a

Nonce

1,762,329,117

Timestamp

11/6/2015, 1:05:47 AM

Confirmations

5,530,091

Mined by

⛏️ P2SHAdGutu8rysUDXVYYUtzqmyHGNhR169HKUw

Merkle Root

5e7b1c09d3d03c7c5e4109f4cbf60d4b50551190e0a1c76d2be5fd098bafd482

Transactions (2)

Coinbase6f8d7cc2344496…dc2775282f3c63

1 in → 1 out8.4700 XPM109 B

AdGutu8r…R169HKUw

7f361869ae5415…c4732769bc3bc6

1 in → 11 out159.2705 XPM533 B

AGFwvEDt…62cccZgr Aerru2fP…oiK6jW7f AG8KTnnH…7DjqnMdZ APwwBzej…6eoZPy1L ARMCj2fF…U4DH5gb9

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.

1.174 × 10⁹⁶(97-digit number)

11742312818192913658…55255682818886922239

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

1.174 × 10⁹⁶(97-digit number)

11742312818192913658…55255682818886922239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.174 × 10⁹⁶(97-digit number)

11742312818192913658…55255682818886922241

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

2.348 × 10⁹⁶(97-digit number)

23484625636385827316…10511365637773844479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.348 × 10⁹⁶(97-digit number)

23484625636385827316…10511365637773844481

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

4.696 × 10⁹⁶(97-digit number)

46969251272771654633…21022731275547688959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.696 × 10⁹⁶(97-digit number)

46969251272771654633…21022731275547688961

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

9.393 × 10⁹⁶(97-digit number)

93938502545543309266…42045462551095377919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.393 × 10⁹⁶(97-digit number)

93938502545543309266…42045462551095377921

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

1.878 × 10⁹⁷(98-digit number)

18787700509108661853…84090925102190755839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.878 × 10⁹⁷(98-digit number)

18787700509108661853…84090925102190755841

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 #1,314,779

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