Block #298,091

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 2:23:45 AM · Difficulty 9.9919 · 6,501,284 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8c7e8d2c54eb709a129ca955390e357bc6b7a6ed9a9301925b091cf32093428b

View on Chainz ↗

Height

#298,091

Difficulty

9.991928

Transactions

Size

1.14 KB

Version

Bits

09fdef04

Nonce

121,658

Timestamp

12/7/2013, 2:23:45 AM

Confirmations

6,501,284

Mined by

⛏️ kaRGAHuJ9wYhTJUvyVGtJfHi8VJT6eBGmgHrKZ

Merkle Root

b988b0927427ff99f9a240b1d384c9be76014b7014a0bed2b03590b316893b5a

Transactions (1)

Coinbaseb988b0927427ff…3590b316893b5a

1 in → 30 out9.9800 XPM1.06 KB

AHuJ9wYh…BGmgHrKZ APw6W8tk…RgVVbThY AKEwr54i…9BfmMkRh ASh9do5c…cndGfXb4 AcC2zSod…rtWatH79

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.

9.378 × 10⁸⁸(89-digit number)

93787655724492363807…57869946076831862479

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

9.378 × 10⁸⁸(89-digit number)

93787655724492363807…57869946076831862479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.378 × 10⁸⁸(89-digit number)

93787655724492363807…57869946076831862481

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

1.875 × 10⁸⁹(90-digit number)

18757531144898472761…15739892153663724959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.875 × 10⁸⁹(90-digit number)

18757531144898472761…15739892153663724961

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

3.751 × 10⁸⁹(90-digit number)

37515062289796945522…31479784307327449919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.751 × 10⁸⁹(90-digit number)

37515062289796945522…31479784307327449921

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

7.503 × 10⁸⁹(90-digit number)

75030124579593891045…62959568614654899839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.503 × 10⁸⁹(90-digit number)

75030124579593891045…62959568614654899841

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

1.500 × 10⁹⁰(91-digit number)

15006024915918778209…25919137229309799679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.500 × 10⁹⁰(91-digit number)

15006024915918778209…25919137229309799681

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