Block #1,809,525

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/15/2016, 10:23:57 PM · Difficulty 10.8111 · 5,017,711 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ee1885194443b18dbcefde460969437d0a1080b19b75edee26bcae383b0f558e

View on Chainz ↗

Height

#1,809,525

Difficulty

10.811052

Transactions

Size

243 B

Version

Bits

0acfa119

Nonce

34,891,905

Timestamp

10/15/2016, 10:23:57 PM

Confirmations

5,017,711

Mined by

⛏️ P2SHATd5Bq5SNppozp9HDzLQKxc4KVPcfPgHVj

Merkle Root

24b5325c2e1edeabed13737c109591e78700831f1b5bf041ad07408d395f3a26

Transactions (1)

Coinbase24b5325c2e1ede…07408d395f3a26

1 in → 2 out8.5400 XPM152 B

ATd5Bq5S…PcfPgHVj ALPu3s2c…EJXLjVFh

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.

3.700 × 10⁹⁶(97-digit number)

37004593934366295157…86564272648803814399

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

3.700 × 10⁹⁶(97-digit number)

37004593934366295157…86564272648803814399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.700 × 10⁹⁶(97-digit number)

37004593934366295157…86564272648803814401

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

7.400 × 10⁹⁶(97-digit number)

74009187868732590315…73128545297607628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.400 × 10⁹⁶(97-digit number)

74009187868732590315…73128545297607628801

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

1.480 × 10⁹⁷(98-digit number)

14801837573746518063…46257090595215257599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.480 × 10⁹⁷(98-digit number)

14801837573746518063…46257090595215257601

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

2.960 × 10⁹⁷(98-digit number)

29603675147493036126…92514181190430515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.960 × 10⁹⁷(98-digit number)

29603675147493036126…92514181190430515201

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

5.920 × 10⁹⁷(98-digit number)

59207350294986072252…85028362380861030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.920 × 10⁹⁷(98-digit number)

59207350294986072252…85028362380861030401

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

1.184 × 10⁹⁸(99-digit number)

11841470058997214450…70056724761722060799

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 #1,809,525

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