Block #2,469,344

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/12/2018, 11:05:37 AM · Difficulty 10.9601 · 4,371,597 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64c0c81ac9fb27881631773fc65cc4a7f104bf7ee00a75b69fd6f958af8e981c

View on Chainz ↗

Height

#2,469,344

Difficulty

10.960067

Transactions

Size

607 B

Version

Bits

0af5c6f3

Nonce

535,156,227

Timestamp

1/12/2018, 11:05:37 AM

Confirmations

4,371,597

Mined by

⛏️ P2SHARHrVVzL2DPG8gwRTTaNkaaRXGQgV8gbkM

Merkle Root

78bd8bf213776b542a00e5afea6cfe753928be8eeecf0e2846869f9c51a4d141

Transactions (2)

Coinbasee14b9c36edac05…3929ca09d83d3d

1 in → 1 out8.3200 XPM110 B

ARHrVVzL…QgV8gbkM

9e6ce06fa0c04a…a05d00ff44ecab

2 in → 3 out2299.9900 XPM407 B

AHF562Gg…W6tY2jF6 AcPS7phk…E2u4g8rH Af2fLkEA…zDpr7FeB

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.

1.104 × 10⁹⁵(96-digit number)

11049007296668427406…99703909351200923899

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

1.104 × 10⁹⁵(96-digit number)

11049007296668427406…99703909351200923899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.104 × 10⁹⁵(96-digit number)

11049007296668427406…99703909351200923901

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

2.209 × 10⁹⁵(96-digit number)

22098014593336854812…99407818702401847799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.209 × 10⁹⁵(96-digit number)

22098014593336854812…99407818702401847801

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

4.419 × 10⁹⁵(96-digit number)

44196029186673709624…98815637404803695599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.419 × 10⁹⁵(96-digit number)

44196029186673709624…98815637404803695601

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

8.839 × 10⁹⁵(96-digit number)

88392058373347419248…97631274809607391199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.839 × 10⁹⁵(96-digit number)

88392058373347419248…97631274809607391201

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

1.767 × 10⁹⁶(97-digit number)

17678411674669483849…95262549619214782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.767 × 10⁹⁶(97-digit number)

17678411674669483849…95262549619214782401

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

3.535 × 10⁹⁶(97-digit number)

35356823349338967699…90525099238429564799

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 #2,469,344

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