Block #300,858

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 8:07:43 PM · Difficulty 9.9924 · 6,516,363 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bb97b96d88e29ad675e36e0b7807881110ca12b77a8be98982539d753af0e88c

View on Chainz ↗

Height

#300,858

Difficulty

9.992424

Transactions

Size

1.18 KB

Version

Bits

09fe0f87

Nonce

58,170

Timestamp

12/8/2013, 8:07:43 PM

Confirmations

6,516,363

Mined by

⛏️ :aRYAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

f44137e1a2e1239182119999c34937af5ed4c5bf5396056735a405c09582905a

Transactions (1)

Coinbasef44137e1a2e123…a405c09582905a

1 in → 31 out9.9800 XPM1.09 KB

AYtDvcGs…VuAcA7m7 AJzWx2VD…j4ZSMit5 AHCbk3sT…ddhvYDDU AQyr8Lw3…hs4nt3Pn Ac6mGvmQ…XqWmPHjR

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.

2.973 × 10⁹⁷(98-digit number)

29733307687600682003…03162961853660948479

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

2.973 × 10⁹⁷(98-digit number)

29733307687600682003…03162961853660948479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.973 × 10⁹⁷(98-digit number)

29733307687600682003…03162961853660948481

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

5.946 × 10⁹⁷(98-digit number)

59466615375201364006…06325923707321896959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.946 × 10⁹⁷(98-digit number)

59466615375201364006…06325923707321896961

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

1.189 × 10⁹⁸(99-digit number)

11893323075040272801…12651847414643793919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.189 × 10⁹⁸(99-digit number)

11893323075040272801…12651847414643793921

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

2.378 × 10⁹⁸(99-digit number)

23786646150080545602…25303694829287587839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.378 × 10⁹⁸(99-digit number)

23786646150080545602…25303694829287587841

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

4.757 × 10⁹⁸(99-digit number)

47573292300161091205…50607389658575175679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.757 × 10⁹⁸(99-digit number)

47573292300161091205…50607389658575175681

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 #300,858

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