Block #457,368

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 8:34:23 PM · Difficulty 10.4203 · 6,338,917 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

39035c6b01a9df11d552ad33f9c398dcc9e3529d7f2b270c3a64413669e8eae1

View on Chainz ↗

Height

#457,368

Difficulty

10.420253

Transactions

Size

1.80 KB

Version

Bits

0a6b95ac

Nonce

196,265

Timestamp

3/23/2014, 8:34:23 PM

Confirmations

6,338,917

Mined by

⛏️ P2SHAKj8s5aNVs48Ged646QTWvPWdhixLKyxkS

Merkle Root

8ccc0c45c7a3eefbc0beeb4ba64bcbf3bbe61cb08fcde9b33f9d4d92793bdf25

Transactions (3)

Coinbase796d22c9ad76e0…af882fb3b08f24

1 in → 1 out9.2200 XPM111 B

AKj8s5aN…ixLKyxkS

4a069fd4adeb44…808bcee805fea0

6 in → 2 out2.4228 XPM968 B

AN1f1zor…kC158trK AHNLErcL…rhjMkmy2

bc5e1d34f817e7…bbb28c409ff67c

4 in → 2 out2.5800 XPM672 B

ASw2DRpR…MeQCHGv1 AHNLErcL…rhjMkmy2

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.

6.484 × 10⁹⁷(98-digit number)

64842032429198112887…31626007970370954879

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

6.484 × 10⁹⁷(98-digit number)

64842032429198112887…31626007970370954879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.484 × 10⁹⁷(98-digit number)

64842032429198112887…31626007970370954881

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

1.296 × 10⁹⁸(99-digit number)

12968406485839622577…63252015940741909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.296 × 10⁹⁸(99-digit number)

12968406485839622577…63252015940741909761

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

2.593 × 10⁹⁸(99-digit number)

25936812971679245154…26504031881483819519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.593 × 10⁹⁸(99-digit number)

25936812971679245154…26504031881483819521

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

5.187 × 10⁹⁸(99-digit number)

51873625943358490309…53008063762967639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.187 × 10⁹⁸(99-digit number)

51873625943358490309…53008063762967639041

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

1.037 × 10⁹⁹(100-digit number)

10374725188671698061…06016127525935278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.037 × 10⁹⁹(100-digit number)

10374725188671698061…06016127525935278081

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