Block #440,470

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 10:54:44 AM · Difficulty 10.3530 · 6,367,607 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

17e5712f00398e60a399fee552aa7c1d0756a3c6d1aa4dc04961c261c8c4a765

View on Chainz ↗

Height

#440,470

Difficulty

10.352987

Transactions

Size

902 B

Version

Bits

0a5a5d5b

Nonce

1,195

Timestamp

3/12/2014, 10:54:44 AM

Confirmations

6,367,607

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

8f9e795f9d7e3c27aa2ddfdb85581bf653f7d57bf6d5b79e132a02de004b293b

Transactions (1)

Coinbase8f9e795f9d7e3c…2a02de004b293b

1 in → 22 out9.3200 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

8.593 × 10⁹⁷(98-digit number)

85935021500253093693…46570742502307635199

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

8.593 × 10⁹⁷(98-digit number)

85935021500253093693…46570742502307635199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.593 × 10⁹⁷(98-digit number)

85935021500253093693…46570742502307635201

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

1.718 × 10⁹⁸(99-digit number)

17187004300050618738…93141485004615270399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.718 × 10⁹⁸(99-digit number)

17187004300050618738…93141485004615270401

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

3.437 × 10⁹⁸(99-digit number)

34374008600101237477…86282970009230540799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.437 × 10⁹⁸(99-digit number)

34374008600101237477…86282970009230540801

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

6.874 × 10⁹⁸(99-digit number)

68748017200202474954…72565940018461081599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.874 × 10⁹⁸(99-digit number)

68748017200202474954…72565940018461081601

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

1.374 × 10⁹⁹(100-digit number)

13749603440040494990…45131880036922163199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.374 × 10⁹⁹(100-digit number)

13749603440040494990…45131880036922163201

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 #440,470

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