Block #859,043

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/19/2014, 3:01:04 AM · Difficulty 10.9660 · 5,958,315 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5705167e9913d81979133660753a9a9fe89f6d42c6b3f801c7f306fceb54652

View on Chainz ↗

Height

#859,043

Difficulty

10.966029

Transactions

Size

17.34 KB

Version

Bits

0af74da8

Nonce

821,893,903

Timestamp

12/19/2014, 3:01:04 AM

Confirmations

5,958,315

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c3624f956ac9fc339072475f599624b741005cd99b9921b9a182bd5ef8aea1d5

Transactions (2)

Coinbasececfa26cc956c7…51b67da7e4cfff

1 in → 1 out8.7100 XPM116 B

ANSXnLY2…Sd25TjkD

5c6b9fdb7a3c68…2a9075b7c80c8c

118 in → 2 out18.8622 XPM17.14 KB

ALXG2RoL…zFPo5wgQ AY1We4vh…BefNQDuT

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.

8.031 × 10⁹⁸(99-digit number)

80314536769679947307…95515828518152110079

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

8.031 × 10⁹⁸(99-digit number)

80314536769679947307…95515828518152110079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.031 × 10⁹⁸(99-digit number)

80314536769679947307…95515828518152110081

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

1.606 × 10⁹⁹(100-digit number)

16062907353935989461…91031657036304220159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.606 × 10⁹⁹(100-digit number)

16062907353935989461…91031657036304220161

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

3.212 × 10⁹⁹(100-digit number)

32125814707871978923…82063314072608440319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.212 × 10⁹⁹(100-digit number)

32125814707871978923…82063314072608440321

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

6.425 × 10⁹⁹(100-digit number)

64251629415743957846…64126628145216880639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.425 × 10⁹⁹(100-digit number)

64251629415743957846…64126628145216880641

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

1.285 × 10¹⁰⁰(101-digit number)

12850325883148791569…28253256290433761279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.285 × 10¹⁰⁰(101-digit number)

12850325883148791569…28253256290433761281

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

2.570 × 10¹⁰⁰(101-digit number)

25700651766297583138…56506512580867522559

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 #859,043

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