Block #151,587

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/5/2013, 6:33:19 PM · Difficulty 9.8614 · 6,654,168 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

995f46f3fea39beaa996f8bfa47849a8867a31674fcb90113eb2677967fd817e

View on Chainz ↗

Height

#151,587

Difficulty

9.861352

Transactions

Size

1001 B

Version

Bits

09dc8196

Nonce

199,176

Timestamp

9/5/2013, 6:33:19 PM

Confirmations

6,654,168

Mined by

⛏️ P2SHAP91QEDQfufBUohT6sogfnRJN9W6JZAB9n

Merkle Root

a2160239583af1301f9ce4dd28a6d572e9cd64d924f08fa23b94eeb0e85f75dc

Transactions (3)

Coinbase92c17807ce1fe3…2699d5fb32e958

1 in → 1 out10.2900 XPM109 B

AP91QEDQ…W6JZAB9n

04c547680da9d1…34ff1c6f4a36fc

4 in → 1 out41.5000 XPM497 B

AbHtjXf6…GZGxhj1y

6c221203a8293e…2cea58f12105a5

2 in → 1 out15.4900 XPM306 B

AbHtjXf6…GZGxhj1y

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.

3.620 × 10⁹¹(92-digit number)

36203057489736976643…64888565384931283359

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

3.620 × 10⁹¹(92-digit number)

36203057489736976643…64888565384931283359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.620 × 10⁹¹(92-digit number)

36203057489736976643…64888565384931283361

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

7.240 × 10⁹¹(92-digit number)

72406114979473953286…29777130769862566719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.240 × 10⁹¹(92-digit number)

72406114979473953286…29777130769862566721

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

1.448 × 10⁹²(93-digit number)

14481222995894790657…59554261539725133439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.448 × 10⁹²(93-digit number)

14481222995894790657…59554261539725133441

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

2.896 × 10⁹²(93-digit number)

28962445991789581314…19108523079450266879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.896 × 10⁹²(93-digit number)

28962445991789581314…19108523079450266881

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

5.792 × 10⁹²(93-digit number)

57924891983579162629…38217046158900533759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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