Block #468,420

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2014, 12:19:24 PM · Difficulty 10.4299 · 6,334,112 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b62a4747f78e078dd5708efd3791a4a79c24091323105559f507e86f722613d

View on Chainz ↗

Height

#468,420

Difficulty

10.429942

Transactions

Size

969 B

Version

Bits

0a6e10b4

Nonce

6,178

Timestamp

3/31/2014, 12:19:24 PM

Confirmations

6,334,112

Mined by

⛏️ %aS9AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1c4fe82d9661619793f86f559d74006d2ef4482de3c3befad2a46b6c9a42a9b4

Transactions (1)

Coinbase1c4fe82d966161…a46b6c9a42a9b4

1 in → 24 out9.1800 XPM879 B

AQvZBsUo…hppgRZTJ ASAv2svc…JNebh6Lj ANeHTs9o…oazVAG8Z AdwTEXyC…NwbVbqZV AQ8QAT3J…rCFKuVbR

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.

4.658 × 10⁹³(94-digit number)

46581065572791559552…79333895279501833579

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

4.658 × 10⁹³(94-digit number)

46581065572791559552…79333895279501833579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.658 × 10⁹³(94-digit number)

46581065572791559552…79333895279501833581

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

9.316 × 10⁹³(94-digit number)

93162131145583119104…58667790559003667159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.316 × 10⁹³(94-digit number)

93162131145583119104…58667790559003667161

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

1.863 × 10⁹⁴(95-digit number)

18632426229116623820…17335581118007334319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.863 × 10⁹⁴(95-digit number)

18632426229116623820…17335581118007334321

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

3.726 × 10⁹⁴(95-digit number)

37264852458233247641…34671162236014668639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.726 × 10⁹⁴(95-digit number)

37264852458233247641…34671162236014668641

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

7.452 × 10⁹⁴(95-digit number)

74529704916466495283…69342324472029337279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.452 × 10⁹⁴(95-digit number)

74529704916466495283…69342324472029337281

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