Block #308,491

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 3:27:45 AM · Difficulty 9.9945 · 6,502,579 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70d1013d18097f3912cafd599d7c00ae7c18f195c82a79589f0a37fe8bc5a19e

View on Chainz ↗

Height

#308,491

Difficulty

9.994511

Transactions

Size

1.11 KB

Version

Bits

09fe984b

Nonce

23,037

Timestamp

12/13/2013, 3:27:45 AM

Confirmations

6,502,579

Mined by

⛏️ aR~3Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

fb914251510b37fd2e9ac93d9dbc9f7aaa07ed17c51bbb545cd09ca62102aad0

Transactions (1)

Coinbasefb914251510b37…d09ca62102aad0

1 in → 29 out9.9800 XPM1.02 KB

Aac9Hjdg…P4ktypc3 AYcLTeXR…bscgPops AVzt9k7A…PefCkEea AKwqFUdz…D4jGNKFN AWzfZcmd…eSsQZosZ

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.

7.439 × 10⁹¹(92-digit number)

74392821267997601036…38154653984992499199

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

7.439 × 10⁹¹(92-digit number)

74392821267997601036…38154653984992499199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.439 × 10⁹¹(92-digit number)

74392821267997601036…38154653984992499201

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

1.487 × 10⁹²(93-digit number)

14878564253599520207…76309307969984998399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.487 × 10⁹²(93-digit number)

14878564253599520207…76309307969984998401

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

2.975 × 10⁹²(93-digit number)

29757128507199040414…52618615939969996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.975 × 10⁹²(93-digit number)

29757128507199040414…52618615939969996801

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

5.951 × 10⁹²(93-digit number)

59514257014398080828…05237231879939993599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.951 × 10⁹²(93-digit number)

59514257014398080828…05237231879939993601

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

1.190 × 10⁹³(94-digit number)

11902851402879616165…10474463759879987199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.190 × 10⁹³(94-digit number)

11902851402879616165…10474463759879987201

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

Block #308,491

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