Block #866,444

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/24/2014, 2:43:48 PM · Difficulty 10.9627 · 5,964,793 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9fea8583d18e39a0653d9c31bb247f6c2d5e99ecc90254d9a0907210134f3ed8

View on Chainz ↗

Height

#866,444

Difficulty

10.962679

Transactions

Size

22.97 KB

Version

Bits

0af6721a

Nonce

260,905,846

Timestamp

12/24/2014, 2:43:48 PM

Confirmations

5,964,793

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7ea826e459d873acea72d8229c48d0d510eca91a49a01e2ccf49ecc3d3706291

Transactions (2)

Coinbase72008645dd384b…85bd8c7787b369

1 in → 1 out8.6400 XPM116 B

ANSXnLY2…Sd25TjkD

bbf2c51b2786db…832388792c4196

157 in → 2 out22.5130 XPM22.77 KB

AYbQUuPy…ngBocWSr AHkMsp9M…eE3YFqnW

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.

2.689 × 10⁹⁷(98-digit number)

26894070767282065993…89346552152197816319

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

2.689 × 10⁹⁷(98-digit number)

26894070767282065993…89346552152197816319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.689 × 10⁹⁷(98-digit number)

26894070767282065993…89346552152197816321

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

5.378 × 10⁹⁷(98-digit number)

53788141534564131987…78693104304395632639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.378 × 10⁹⁷(98-digit number)

53788141534564131987…78693104304395632641

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

1.075 × 10⁹⁸(99-digit number)

10757628306912826397…57386208608791265279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.075 × 10⁹⁸(99-digit number)

10757628306912826397…57386208608791265281

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

2.151 × 10⁹⁸(99-digit number)

21515256613825652795…14772417217582530559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.151 × 10⁹⁸(99-digit number)

21515256613825652795…14772417217582530561

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

4.303 × 10⁹⁸(99-digit number)

43030513227651305590…29544834435165061119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.303 × 10⁹⁸(99-digit number)

43030513227651305590…29544834435165061121

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

8.606 × 10⁹⁸(99-digit number)

86061026455302611180…59089668870330122239

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 #866,444

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