Block #186,444

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 10:09:59 PM · Difficulty 9.8658 · 6,609,433 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

661eb17a0c6f2b390dd165c154465cfd2f2aea3713dc040673b9ffe887c372a4

View on Chainz ↗

Height

#186,444

Difficulty

9.865817

Transactions

Size

584 B

Version

Bits

09dda628

Nonce

53,372

Timestamp

9/29/2013, 10:09:59 PM

Confirmations

6,609,433

Mined by

⛏️ P2SHAWsEijaAmPVVY4otUbJH1Yqtdf9WbDL6tH

Merkle Root

bdf0f2e77284599884c31a2c11848a320421195b96938ca9dfd15e1c4cf54a2b

Transactions (3)

Coinbase4c853772fe83e5…1f3edc2e40baa9

1 in → 1 out10.2800 XPM109 B

AWsEijaA…9WbDL6tH

e5c16c512f32af…7d492a4cf047d2

1 in → 1 out10.2700 XPM158 B

AcWWWPc4…NKmGSdQs

c0077cb4f5ff0a…59e55929be44e2

1 in → 2 out7.9924 XPM226 B

AQ1zBE8p…VtgAEDWW ALc2ZNEa…21qTLT94

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.

1.311 × 10⁹⁸(99-digit number)

13111237595247914083…83584337490755589119

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

1.311 × 10⁹⁸(99-digit number)

13111237595247914083…83584337490755589119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.311 × 10⁹⁸(99-digit number)

13111237595247914083…83584337490755589121

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

2.622 × 10⁹⁸(99-digit number)

26222475190495828166…67168674981511178239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.622 × 10⁹⁸(99-digit number)

26222475190495828166…67168674981511178241

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

5.244 × 10⁹⁸(99-digit number)

52444950380991656333…34337349963022356479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.244 × 10⁹⁸(99-digit number)

52444950380991656333…34337349963022356481

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

1.048 × 10⁹⁹(100-digit number)

10488990076198331266…68674699926044712959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.048 × 10⁹⁹(100-digit number)

10488990076198331266…68674699926044712961

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

2.097 × 10⁹⁹(100-digit number)

20977980152396662533…37349399852089425919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.097 × 10⁹⁹(100-digit number)

20977980152396662533…37349399852089425921

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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