Block #301,440

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 4:55:18 AM · Difficulty 9.9925 · 6,492,827 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24a21d63f63e14adc459017f80eede613a2812b28c726447172ff4b9d72e2b61

View on Chainz ↗

Height

#301,440

Difficulty

9.992524

Transactions

Size

1.12 KB

Version

Bits

09fe160c

Nonce

21,842

Timestamp

12/9/2013, 4:55:18 AM

Confirmations

6,492,827

Merkle Root

bee672a1f8ed65eb06e9687f467fd6b2980e86a21b92610e5c869562fe51fbb1

Transactions (2)

Coinbase2c0882cb8093f7…ba1a931cfd1ce7

1 in → 1 out10.0100 XPM109 B

AX2TVgXP…4oFqomRn

7cebaf2f9dd584…3274c8bfb7a955

5 in → 8 out21.1612 XPM951 B

AKLyn6AN…ryhMEqf9 AK2Fed2M…L8dDr8s4 ARC3GLtb…BSXvSmKg AdYH33yX…NKufJznD ATz1Sryu…PWZHWKYx

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.

2.729 × 10⁹³(94-digit number)

27293186563590635259…03777408749089357119

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

2.729 × 10⁹³(94-digit number)

27293186563590635259…03777408749089357119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.729 × 10⁹³(94-digit number)

27293186563590635259…03777408749089357121

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

5.458 × 10⁹³(94-digit number)

54586373127181270518…07554817498178714239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.458 × 10⁹³(94-digit number)

54586373127181270518…07554817498178714241

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

1.091 × 10⁹⁴(95-digit number)

10917274625436254103…15109634996357428479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.091 × 10⁹⁴(95-digit number)

10917274625436254103…15109634996357428481

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

2.183 × 10⁹⁴(95-digit number)

21834549250872508207…30219269992714856959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.183 × 10⁹⁴(95-digit number)

21834549250872508207…30219269992714856961

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

4.366 × 10⁹⁴(95-digit number)

43669098501745016414…60438539985429713919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.366 × 10⁹⁴(95-digit number)

43669098501745016414…60438539985429713921

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