Block #293,036

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 2:19:45 AM · Difficulty 9.9905 · 6,511,159 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95cd799059fde126060a1e41b2e05e618d60899078a904992d1fe958be9aaa85

View on Chainz ↗

Height

#293,036

Difficulty

9.990484

Transactions

Size

2.72 KB

Version

Bits

09fd905e

Nonce

365,379

Timestamp

12/4/2013, 2:19:45 AM

Confirmations

6,511,159

Mined by

⛏️ xaRAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

c0f105a0834a02d778c85862e05636589599663832c2cbbc1e8c54f703e1b444

Transactions (4)

Coinbase3a2aaaeba811fa…64489e2e4382e4

1 in → 30 out9.9800 XPM1.06 KB

AZninDSu…FvgDMwC4 ARzXge7S…CEjL5oYm APFsQ3Fo…xoFKrF12 ARcqMJhp…RVLToQ6S ARskhKeb…UgDvvX9P

be4520dca7721e…3414b94ef64cb3

1 in → 1 out10.2600 XPM158 B

ATV4M1CV…dd9zw8nH

ef0923f3f5bc75…32d4e7b2db7b9d

5 in → 2 out5.3227 XPM819 B

AHtmvgn5…Rc2kjm5q AeEFDbAk…Qf2gWWpR

1fae8d3625b8ec…d494d1b48f1880

4 in → 1 out3.2000 XPM635 B

AYv42jN6…ryboZAEg

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.

3.536 × 10⁹³(94-digit number)

35363935139011219835…22186168212600012799

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

3.536 × 10⁹³(94-digit number)

35363935139011219835…22186168212600012799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.536 × 10⁹³(94-digit number)

35363935139011219835…22186168212600012801

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

7.072 × 10⁹³(94-digit number)

70727870278022439671…44372336425200025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.072 × 10⁹³(94-digit number)

70727870278022439671…44372336425200025601

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

1.414 × 10⁹⁴(95-digit number)

14145574055604487934…88744672850400051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.414 × 10⁹⁴(95-digit number)

14145574055604487934…88744672850400051201

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

2.829 × 10⁹⁴(95-digit number)

28291148111208975868…77489345700800102399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.829 × 10⁹⁴(95-digit number)

28291148111208975868…77489345700800102401

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

5.658 × 10⁹⁴(95-digit number)

56582296222417951737…54978691401600204799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.658 × 10⁹⁴(95-digit number)

56582296222417951737…54978691401600204801

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