Block #3,170,483

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/6/2019, 10:18:41 AM · Difficulty 11.3122 · 3,673,597 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3945f1ab5df7058763fcd75ea458daa5b7508ce6484a20a549efe8c413d6d56a

View on Chainz ↗

Height

#3,170,483

Difficulty

11.312222

Transactions

Size

1.57 KB

Version

Bits

0b4fedc1

Nonce

717,687,407

Timestamp

5/6/2019, 10:18:41 AM

Confirmations

3,673,597

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

d2fe242895460d1c51124f7dfc259291407d517952dcd73532c936e8528860d3

Transactions (2)

Coinbasefd400b111fcaaa…f5f0e7434be7c9

1 in → 1 out7.8200 XPM110 B

AbXwmGxD…4XXYP765

46877b860df71c…40685a509b0c16

9 in → 2 out1000.0100 XPM1.38 KB

ANQcL7Nm…sf4oQq15 AVXqS2Up…BeYxHbyP

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.

5.294 × 10⁹⁷(98-digit number)

52946316838563814071…05553419266533294079

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

5.294 × 10⁹⁷(98-digit number)

52946316838563814071…05553419266533294079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.294 × 10⁹⁷(98-digit number)

52946316838563814071…05553419266533294081

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

1.058 × 10⁹⁸(99-digit number)

10589263367712762814…11106838533066588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.058 × 10⁹⁸(99-digit number)

10589263367712762814…11106838533066588161

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

2.117 × 10⁹⁸(99-digit number)

21178526735425525628…22213677066133176319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.117 × 10⁹⁸(99-digit number)

21178526735425525628…22213677066133176321

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

4.235 × 10⁹⁸(99-digit number)

42357053470851051257…44427354132266352639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.235 × 10⁹⁸(99-digit number)

42357053470851051257…44427354132266352641

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

8.471 × 10⁹⁸(99-digit number)

84714106941702102514…88854708264532705279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.471 × 10⁹⁸(99-digit number)

84714106941702102514…88854708264532705281

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

1.694 × 10⁹⁹(100-digit number)

16942821388340420502…77709416529065410559

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 #3,170,483

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