Block #2,759,858

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/22/2018, 6:20:16 AM · Difficulty 11.6590 · 4,071,868 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e13f7152e28acc4681235c0a47070965767f41f2e39f3c62bde24a4dcdee9c7c

View on Chainz ↗

Height

#2,759,858

Difficulty

11.658950

Transactions

Size

1.62 KB

Version

Bits

0ba8b0f3

Nonce

361,412,936

Timestamp

7/22/2018, 6:20:16 AM

Confirmations

4,071,868

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

d098ad4bb2873b1a22f87c1be3dcf4ca896637b07b987271341235e66ae02102

Transactions (3)

Coinbase17db231d2ae73d…3b713cdcb0957e

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

f237adfb238235…24ac9bf5895037

7 in → 2 out105.4738 XPM1.08 KB

AMacMFhM…iFNVuut4 AK4aMWmv…dDdrYqwd

5de7dca0d4a7ee…ff0128f483153d

2 in → 2 out14.2000 XPM341 B

AcoEVFrA…UMT57m4T AV7eJoTN…pLyuARba

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.

3.987 × 10⁹⁸(99-digit number)

39873830059355181451…64626402294926868479

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

3.987 × 10⁹⁸(99-digit number)

39873830059355181451…64626402294926868479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.987 × 10⁹⁸(99-digit number)

39873830059355181451…64626402294926868481

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

7.974 × 10⁹⁸(99-digit number)

79747660118710362903…29252804589853736959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.974 × 10⁹⁸(99-digit number)

79747660118710362903…29252804589853736961

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

1.594 × 10⁹⁹(100-digit number)

15949532023742072580…58505609179707473919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.594 × 10⁹⁹(100-digit number)

15949532023742072580…58505609179707473921

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

3.189 × 10⁹⁹(100-digit number)

31899064047484145161…17011218359414947839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.189 × 10⁹⁹(100-digit number)

31899064047484145161…17011218359414947841

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

6.379 × 10⁹⁹(100-digit number)

63798128094968290322…34022436718829895679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.379 × 10⁹⁹(100-digit number)

63798128094968290322…34022436718829895681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.275 × 10¹⁰⁰(101-digit number)

12759625618993658064…68044873437659791359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,759,858

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