Block #299,893

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 6:26:51 AM · Difficulty 9.9922 · 6,494,805 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a554f32812ec2ffeb6c0d61f969c93081bdb847486e605d6c26893d1942fb90b

View on Chainz ↗

Height

#299,893

Difficulty

9.992177

Transactions

Size

1.11 KB

Version

Bits

09fdff51

Nonce

49,879

Timestamp

12/8/2013, 6:26:51 AM

Confirmations

6,494,805

Mined by

⛏️ uaRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

57f17af8d138cba962c28d00bf6133485a50f72cd79b8676aa0776560c4359b9

Transactions (1)

Coinbase57f17af8d138cb…0776560c4359b9

1 in → 29 out9.9800 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz AHuJ9wYh…BGmgHrKZ AQf7sjuh…sNY5fXpu AbyCQTA5…7TFD6FSM AMBbmvEz…yFqmSmw2

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.

3.002 × 10⁹⁴(95-digit number)

30020298013661050900…81502695920523342399

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

3.002 × 10⁹⁴(95-digit number)

30020298013661050900…81502695920523342399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.002 × 10⁹⁴(95-digit number)

30020298013661050900…81502695920523342401

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

6.004 × 10⁹⁴(95-digit number)

60040596027322101800…63005391841046684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.004 × 10⁹⁴(95-digit number)

60040596027322101800…63005391841046684801

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

1.200 × 10⁹⁵(96-digit number)

12008119205464420360…26010783682093369599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.200 × 10⁹⁵(96-digit number)

12008119205464420360…26010783682093369601

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

2.401 × 10⁹⁵(96-digit number)

24016238410928840720…52021567364186739199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.401 × 10⁹⁵(96-digit number)

24016238410928840720…52021567364186739201

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

4.803 × 10⁹⁵(96-digit number)

48032476821857681440…04043134728373478399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.803 × 10⁹⁵(96-digit number)

48032476821857681440…04043134728373478401

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