Block #302,620

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 10:15:20 PM · Difficulty 9.9928 · 6,512,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ca8de0699e359ff7a00597964838a8ac9b4cb68b47c662457a80142ded0a5eb

View on Chainz ↗

Height

#302,620

Difficulty

9.992766

Transactions

Size

1.15 KB

Version

Bits

09fe25e5

Nonce

93,260

Timestamp

12/9/2013, 10:15:20 PM

Confirmations

6,512,292

Mined by

⛏️ aR@AYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

caece825c3b15e2f1ada870e22ffee0553ef09edb3b4bd4232c08bc378a12898

Transactions (1)

Coinbasecaece825c3b15e…c08bc378a12898

1 in → 30 out9.9800 XPM1.06 KB

AYtDvcGs…VuAcA7m7 AJzWx2VD…j4ZSMit5 AQf7sjuh…sNY5fXpu Aekx7F9R…HJmj5ecv AYckRkCF…TgDe5VSp

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.

7.445 × 10⁹³(94-digit number)

74453477919803127825…83576241385541464719

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

7.445 × 10⁹³(94-digit number)

74453477919803127825…83576241385541464719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.445 × 10⁹³(94-digit number)

74453477919803127825…83576241385541464721

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

1.489 × 10⁹⁴(95-digit number)

14890695583960625565…67152482771082929439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.489 × 10⁹⁴(95-digit number)

14890695583960625565…67152482771082929441

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

2.978 × 10⁹⁴(95-digit number)

29781391167921251130…34304965542165858879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.978 × 10⁹⁴(95-digit number)

29781391167921251130…34304965542165858881

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

5.956 × 10⁹⁴(95-digit number)

59562782335842502260…68609931084331717759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.956 × 10⁹⁴(95-digit number)

59562782335842502260…68609931084331717761

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

1.191 × 10⁹⁵(96-digit number)

11912556467168500452…37219862168663435519

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

Block #302,620

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