Block #87,571

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 12:15:41 AM · Difficulty 9.2727 · 6,707,219 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fd282659376dbc98ff127d81a0e615a175ab692b1263233efffa7f8f10d9a59

View on Chainz ↗

Height

#87,571

Difficulty

9.272708

Transactions

Size

771 B

Version

Bits

0945d032

Nonce

4,709

Timestamp

7/29/2013, 12:15:41 AM

Confirmations

6,707,219

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

dd6bd98ec3385c5c965babefd3183a09d6e548331b8c5926e1b0460b5dd4e9f2

Transactions (2)

Coinbasef3fd50dbf5b3b8…ba400d6b692325

1 in → 1 out11.6200 XPM109 B

AcuJraLT…Y66BS47Q

b18c799fdbe9f7…f3832a8497c34f

4 in → 2 out36.2500 XPM570 B

AWCpn94W…AVCFuzza AY85jtxh…cgBXGaRN

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.

3.028 × 10⁹⁸(99-digit number)

30284371182005662672…70012074190368971439

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

3.028 × 10⁹⁸(99-digit number)

30284371182005662672…70012074190368971439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.028 × 10⁹⁸(99-digit number)

30284371182005662672…70012074190368971441

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

6.056 × 10⁹⁸(99-digit number)

60568742364011325345…40024148380737942879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.056 × 10⁹⁸(99-digit number)

60568742364011325345…40024148380737942881

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

1.211 × 10⁹⁹(100-digit number)

12113748472802265069…80048296761475885759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.211 × 10⁹⁹(100-digit number)

12113748472802265069…80048296761475885761

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

2.422 × 10⁹⁹(100-digit number)

24227496945604530138…60096593522951771519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.422 × 10⁹⁹(100-digit number)

24227496945604530138…60096593522951771521

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

4.845 × 10⁹⁹(100-digit number)

48454993891209060276…20193187045903543039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.845 × 10⁹⁹(100-digit number)

48454993891209060276…20193187045903543041

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