Block #302,040

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 2:15:11 PM · Difficulty 9.9926 · 6,501,262 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d05f50083d6d5192cbb1d870d8336bee9c2512f30ecbeac895f81962a2fc38f8

View on Chainz ↗

Height

#302,040

Difficulty

9.992602

Transactions

Size

1.93 KB

Version

Bits

09fe1b2d

Nonce

22,229

Timestamp

12/9/2013, 2:15:11 PM

Confirmations

6,501,262

Mined by

⛏️ aRAGjXRvvnJUd1NPyuKWSYGjZPwpdL3EHMT1

Merkle Root

8e1f183318305a4306c6311895354b73f5c22f42e90161521f636bdf661a47ea

Transactions (4)

Coinbase938a63daa5e52c…98d0fa64a7fbe7

1 in → 25 out10.0000 XPM913 B

AGjXRvvn…dL3EHMT1 APgWZwJ2…1nTrECFn AcVAEuoP…1jK61Unr AHuJ9wYh…BGmgHrKZ AdBDetrJ…ayf6m3Ce

0853657ce9ef95…b44685db30da2a

3 in → 2 out28.9198 XPM523 B

Abxn3EEB…8ccf7zVj AUj2yDgV…tSPRAC6E

ff7aeb32e97ef2…dddb7a3896e913

1 in → 2 out8.9569 XPM226 B

ALrHwPSa…tUKYrjvQ AKUEaUvA…6nAqWbP5

508365b510fd92…dc35181c17b838

1 in → 2 out8.9286 XPM227 B

AFreewNR…WwhUuhEf AadurNMG…cjuRvjK9

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.

5.636 × 10⁹¹(92-digit number)

56362007322550151829…68154132919602359039

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

5.636 × 10⁹¹(92-digit number)

56362007322550151829…68154132919602359039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.636 × 10⁹¹(92-digit number)

56362007322550151829…68154132919602359041

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

1.127 × 10⁹²(93-digit number)

11272401464510030365…36308265839204718079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.127 × 10⁹²(93-digit number)

11272401464510030365…36308265839204718081

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

2.254 × 10⁹²(93-digit number)

22544802929020060731…72616531678409436159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.254 × 10⁹²(93-digit number)

22544802929020060731…72616531678409436161

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

4.508 × 10⁹²(93-digit number)

45089605858040121463…45233063356818872319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.508 × 10⁹²(93-digit number)

45089605858040121463…45233063356818872321

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

9.017 × 10⁹²(93-digit number)

90179211716080242927…90466126713637744639

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