Block #444,754

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 10:58:59 AM · Difficulty 10.3510 · 6,400,444 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eed909b7c17e14efb1d75a7f4cbf3d15cafea07fadfe5fe115125532e4faa9ae

View on Chainz ↗

Height

#444,754

Difficulty

10.351005

Transactions

Size

936 B

Version

Bits

0a59db7a

Nonce

21,072

Timestamp

3/15/2014, 10:58:59 AM

Confirmations

6,400,444

Mined by

⛏️ RaS$23AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d077063ef744d2c75502d4240d8a0b84ef04d86ec4532557a7a36711f19aa3a6

Transactions (1)

Coinbased077063ef744d2…a36711f19aa3a6

1 in → 23 out9.3200 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

8.823 × 10⁹⁷(98-digit number)

88231091882938423827…95461863089192299379

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

8.823 × 10⁹⁷(98-digit number)

88231091882938423827…95461863089192299379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.823 × 10⁹⁷(98-digit number)

88231091882938423827…95461863089192299381

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

1.764 × 10⁹⁸(99-digit number)

17646218376587684765…90923726178384598759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.764 × 10⁹⁸(99-digit number)

17646218376587684765…90923726178384598761

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

3.529 × 10⁹⁸(99-digit number)

35292436753175369530…81847452356769197519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.529 × 10⁹⁸(99-digit number)

35292436753175369530…81847452356769197521

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

7.058 × 10⁹⁸(99-digit number)

70584873506350739061…63694904713538395039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.058 × 10⁹⁸(99-digit number)

70584873506350739061…63694904713538395041

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

1.411 × 10⁹⁹(100-digit number)

14116974701270147812…27389809427076790079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.411 × 10⁹⁹(100-digit number)

14116974701270147812…27389809427076790081

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 #444,754

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