Block #1,368,320

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/13/2015, 8:05:46 PM · Difficulty 10.8359 · 5,462,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c72d0c2495c6cd53e43d0be069857ca027d6c2e87642a96cf7b5b81b3f5a7214

View on Chainz ↗

Height

#1,368,320

Difficulty

10.835869

Transactions

Size

4.82 KB

Version

Bits

0ad5fb7f

Nonce

1,130,102,393

Timestamp

12/13/2015, 8:05:46 PM

Confirmations

5,462,131

Mined by

⛏️ P2SHAY6uF7LwZiuAqvBcKf43D83rkqMUJbkXfa

Merkle Root

022a2144ace5738377bb20fad7563ae2aa12a14488655f15d41f16dc66393bf1

Transactions (3)

Coinbasec0224f6541affa…5b345b213c3383

1 in → 1 out8.5500 XPM110 B

AY6uF7Lw…MUJbkXfa

436b659f61e242…6bdc2d63410ec2

26 in → 2 out178.0115 XPM3.84 KB

AcdVU5yx…QVsWFgWB AbbShyK2…GfDpqsP9

22f4611b23cb92…ada311e5cd6266

1 in → 19 out73.2394 XPM804 B

AcTyYdTB…Au15J5gk AU46crUh…WJty6Nr5 AWWi2VAd…F52EYqWj AHy9zMfo…FPWLULsa AJdhtvrL…F9wUA9XE

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.

3.656 × 10⁹³(94-digit number)

36560202230788950961…98507852448561586879

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

3.656 × 10⁹³(94-digit number)

36560202230788950961…98507852448561586879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.656 × 10⁹³(94-digit number)

36560202230788950961…98507852448561586881

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

7.312 × 10⁹³(94-digit number)

73120404461577901922…97015704897123173759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.312 × 10⁹³(94-digit number)

73120404461577901922…97015704897123173761

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

1.462 × 10⁹⁴(95-digit number)

14624080892315580384…94031409794246347519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.462 × 10⁹⁴(95-digit number)

14624080892315580384…94031409794246347521

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

2.924 × 10⁹⁴(95-digit number)

29248161784631160769…88062819588492695039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.924 × 10⁹⁴(95-digit number)

29248161784631160769…88062819588492695041

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

5.849 × 10⁹⁴(95-digit number)

58496323569262321538…76125639176985390079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.849 × 10⁹⁴(95-digit number)

58496323569262321538…76125639176985390081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.169 × 10⁹⁵(96-digit number)

11699264713852464307…52251278353970780159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,368,320

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