Block #457,939

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 6:09:36 AM · Difficulty 10.4205 · 6,346,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

896be4f985dde71ab9850f0128a80249e258506061ec2b3cf83abd3c662ed60d

View on Chainz ↗

Height

#457,939

Difficulty

10.420528

Transactions

Size

970 B

Version

Bits

0a6ba7bf

Nonce

11,473

Timestamp

3/24/2014, 6:09:36 AM

Confirmations

6,346,374

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2c76ff5ef4b8c9b6c45a4ca9eaa61ce8b4aa9c3719623416fa5f5a9224e9402a

Transactions (1)

Coinbase2c76ff5ef4b8c9…5f5a9224e9402a

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AebWhrRm…K61Qrkws

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.

4.805 × 10⁹⁷(98-digit number)

48051976690307393043…10708082083473245199

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

4.805 × 10⁹⁷(98-digit number)

48051976690307393043…10708082083473245199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.805 × 10⁹⁷(98-digit number)

48051976690307393043…10708082083473245201

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

9.610 × 10⁹⁷(98-digit number)

96103953380614786086…21416164166946490399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.610 × 10⁹⁷(98-digit number)

96103953380614786086…21416164166946490401

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

1.922 × 10⁹⁸(99-digit number)

19220790676122957217…42832328333892980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.922 × 10⁹⁸(99-digit number)

19220790676122957217…42832328333892980801

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

3.844 × 10⁹⁸(99-digit number)

38441581352245914434…85664656667785961599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.844 × 10⁹⁸(99-digit number)

38441581352245914434…85664656667785961601

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

7.688 × 10⁹⁸(99-digit number)

76883162704491828868…71329313335571923199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.688 × 10⁹⁸(99-digit number)

76883162704491828868…71329313335571923201

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