Block #1,778,011

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/24/2016, 7:30:39 PM · Difficulty 10.7639 · 5,035,018 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

11f8f882b811c936a9d2a8bd530cc94f32bdd94482046dc803ff2aa15f60728b

View on Chainz ↗

Height

#1,778,011

Difficulty

10.763866

Transactions

Size

5.28 KB

Version

Bits

0ac38cb1

Nonce

1,508,841,918

Timestamp

9/24/2016, 7:30:39 PM

Confirmations

5,035,018

Mined by

⛏️ P2SHAPD6BnnQz1QzzfYAr7NLkqphmYrMaogtQ8

Merkle Root

9ca9b88e64c1f9b44a154c1ab6011b928622649cd3499f72c5abf7ecf55deb5b

Transactions (4)

Coinbase7ad115c687bf6b…2579d131202d3b

1 in → 1 out8.6900 XPM109 B

APD6BnnQ…rMaogtQ8

a549066129fbfc…766421d5f3dd12

1 in → 51 out59.8800 XPM1.85 KB

ARB8Qp9a…kri75dyj ASiscGY1…fk3GQwxb ARhjHwur…ZN6FkD1m AHVGbgNY…xDDUahUQ ASZHgu3J…YxksZyUn

32f1577a94b953…803ffca6a65a6b

1 in → 33 out3.8800 XPM1.25 KB

AWJrh5Mu…hYqPAfL6 AeYH41pQ…otFrCDYG AbdZmLHs…sQ6reNtd Af4W9WTo…ixQmMk1J ANcZpvm8…rbB3hbxC

e89a0fb4c27b61…9249e79e72246a

2 in → 51 out1.6601 XPM1.99 KB

ANQfc5L7…285C2Wpo ARmtenN4…pbD6PWRr AZC8ryR1…yKLdkZsH AG4VDY27…snsWnDCD AeHT234p…dA9rwVne

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.

2.343 × 10⁹⁵(96-digit number)

23432845190165623286…07461683700299026879

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

2.343 × 10⁹⁵(96-digit number)

23432845190165623286…07461683700299026879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.343 × 10⁹⁵(96-digit number)

23432845190165623286…07461683700299026881

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

4.686 × 10⁹⁵(96-digit number)

46865690380331246573…14923367400598053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.686 × 10⁹⁵(96-digit number)

46865690380331246573…14923367400598053761

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

9.373 × 10⁹⁵(96-digit number)

93731380760662493146…29846734801196107519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.373 × 10⁹⁵(96-digit number)

93731380760662493146…29846734801196107521

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

1.874 × 10⁹⁶(97-digit number)

18746276152132498629…59693469602392215039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.874 × 10⁹⁶(97-digit number)

18746276152132498629…59693469602392215041

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

3.749 × 10⁹⁶(97-digit number)

37492552304264997258…19386939204784430079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.749 × 10⁹⁶(97-digit number)

37492552304264997258…19386939204784430081

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 #1,778,011

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