Block #354,044

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/11/2014, 8:00:51 AM · Difficulty 10.3334 · 6,455,428 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5aa186a190106e0a702591417eea7d5b903db5e2218c5de76967ad494e7132f0

View on Chainz ↗

Height

#354,044

Difficulty

10.333445

Transactions

Size

1003 B

Version

Bits

0a555caa

Nonce

4,506

Timestamp

1/11/2014, 8:00:51 AM

Confirmations

6,455,428

Mined by

⛏️ faRxAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

94e66353d917f9d9c05436de347ba7846dcc90e0bb0660dd56dc8d4d79f9d432

Transactions (1)

Coinbase94e66353d917f9…dc8d4d79f9d432

1 in → 25 out9.3500 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AYtDvcGs…VuAcA7m7 AP5UvYhU…vLTDwkdA

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.

3.337 × 10⁹³(94-digit number)

33377704372306216643…17317955027057258559

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

3.337 × 10⁹³(94-digit number)

33377704372306216643…17317955027057258559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.337 × 10⁹³(94-digit number)

33377704372306216643…17317955027057258561

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

6.675 × 10⁹³(94-digit number)

66755408744612433286…34635910054114517119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.675 × 10⁹³(94-digit number)

66755408744612433286…34635910054114517121

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

1.335 × 10⁹⁴(95-digit number)

13351081748922486657…69271820108229034239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.335 × 10⁹⁴(95-digit number)

13351081748922486657…69271820108229034241

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

2.670 × 10⁹⁴(95-digit number)

26702163497844973314…38543640216458068479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.670 × 10⁹⁴(95-digit number)

26702163497844973314…38543640216458068481

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

5.340 × 10⁹⁴(95-digit number)

53404326995689946628…77087280432916136959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.340 × 10⁹⁴(95-digit number)

53404326995689946628…77087280432916136961

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 #354,044

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