Block #3,338,039

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/2/2019, 5:20:39 PM · Difficulty 11.0000 · 3,502,172 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4de551570e1463dcd30a9c4b0683b5597efdacd8c808da68404db8da59a8536

View on Chainz ↗

Height

#3,338,039

Difficulty

11.000000

Transactions

Size

427 B

Version

Bits

0b000000

Nonce

200,401,233

Timestamp

9/2/2019, 5:20:39 PM

Confirmations

3,502,172

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

8fa70c5767a1e0ae6612169334611f721c590a8de194118b68bfb3182c7b0f36

Transactions (2)

Coinbase63f0634523931d…64949cc588a88f

1 in → 1 out8.2600 XPM110 B

ASiq2qtK…VMhmk7yL

f745a4b0dc7aab…1143ec96ad1193

1 in → 2 out297.1056 XPM227 B

APQ9gg1V…H4v8MyZ4 AMLggddy…HpikgH98

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.

5.265 × 10⁹⁵(96-digit number)

52658155491427049784…64975578348558831359

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

5.265 × 10⁹⁵(96-digit number)

52658155491427049784…64975578348558831359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.265 × 10⁹⁵(96-digit number)

52658155491427049784…64975578348558831361

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

1.053 × 10⁹⁶(97-digit number)

10531631098285409956…29951156697117662719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.053 × 10⁹⁶(97-digit number)

10531631098285409956…29951156697117662721

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

2.106 × 10⁹⁶(97-digit number)

21063262196570819913…59902313394235325439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.106 × 10⁹⁶(97-digit number)

21063262196570819913…59902313394235325441

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

4.212 × 10⁹⁶(97-digit number)

42126524393141639827…19804626788470650879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.212 × 10⁹⁶(97-digit number)

42126524393141639827…19804626788470650881

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

8.425 × 10⁹⁶(97-digit number)

84253048786283279655…39609253576941301759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.425 × 10⁹⁶(97-digit number)

84253048786283279655…39609253576941301761

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

1.685 × 10⁹⁷(98-digit number)

16850609757256655931…79218507153882603519

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 #3,338,039

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