Block #851,692

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/13/2014, 12:13:21 PM · Difficulty 10.9704 · 5,987,731 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f84d9d1517ba69bd662fb2bfc3798fc6893a40df0da1ddaaa3cc74ae3924f65

View on Chainz ↗

Height

#851,692

Difficulty

10.970426

Transactions

Size

434 B

Version

Bits

0af86dd0

Nonce

1,771,686,229

Timestamp

12/13/2014, 12:13:21 PM

Confirmations

5,987,731

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

24870ed4e85a4eceea53950f4c390a79aaabb0ede495d970fdcf88b58e40d90c

Transactions (2)

Coinbase1d72a56504a503…880df76fac9d09

1 in → 1 out8.3150 XPM116 B

ANSXnLY2…Sd25TjkD

7a44267bac9a02…28746aa0264116

1 in → 2 out0.1000 XPM227 B

AVbVFQPk…vCQWY7Si ALEg5y4P…bjuDCKU9

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.

1.827 × 10⁹⁸(99-digit number)

18276094069361176043…77947159422576665599

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

1.827 × 10⁹⁸(99-digit number)

18276094069361176043…77947159422576665599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.827 × 10⁹⁸(99-digit number)

18276094069361176043…77947159422576665601

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

3.655 × 10⁹⁸(99-digit number)

36552188138722352086…55894318845153331199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.655 × 10⁹⁸(99-digit number)

36552188138722352086…55894318845153331201

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

7.310 × 10⁹⁸(99-digit number)

73104376277444704173…11788637690306662399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.310 × 10⁹⁸(99-digit number)

73104376277444704173…11788637690306662401

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

1.462 × 10⁹⁹(100-digit number)

14620875255488940834…23577275380613324799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.462 × 10⁹⁹(100-digit number)

14620875255488940834…23577275380613324801

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

2.924 × 10⁹⁹(100-digit number)

29241750510977881669…47154550761226649599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.924 × 10⁹⁹(100-digit number)

29241750510977881669…47154550761226649601

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

5.848 × 10⁹⁹(100-digit number)

58483501021955763338…94309101522453299199

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 #851,692

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