Block #462,675

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 2:19:13 PM · Difficulty 10.4156 · 6,340,913 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b8edba55b0560a455ce0e7fa9cbb9ec8e0d90236eea9599f6862b2cd1b583da

View on Chainz ↗

Height

#462,675

Difficulty

10.415591

Transactions

Size

1.21 KB

Version

Bits

0a6a6432

Nonce

112,730

Timestamp

3/27/2014, 2:19:13 PM

Confirmations

6,340,913

Mined by

⛏️ P2SHAdRFmmXefH53kcZoFyMzU9aaNgm8BJBu5Z

Merkle Root

ac8172f6852381a178db69bf4d2c34eb9f517c84afd2600ed3d61d7d151ca8d6

Transactions (3)

Coinbase44185925860bb2…96e19784962e75

1 in → 1 out9.2200 XPM109 B

AdRFmmXe…m8BJBu5Z

3a57bd2b2a050f…0a4a37e0d3ae93

1 in → 2 out6.1558 XPM225 B

AR3dCt7f…F4QWrmyM AcNfyX9t…hT5WFcoz

bd3a6da7b0fa4e…096f0d8ec73fd5

5 in → 2 out0.5213 XPM818 B

AWs7QXYE…2p1nN9v3 AVtEnc3W…MtfHvUv8

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.

8.550 × 10⁹⁷(98-digit number)

85502105943940700840…12043528295360231999

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

8.550 × 10⁹⁷(98-digit number)

85502105943940700840…12043528295360231999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.550 × 10⁹⁷(98-digit number)

85502105943940700840…12043528295360232001

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

1.710 × 10⁹⁸(99-digit number)

17100421188788140168…24087056590720463999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.710 × 10⁹⁸(99-digit number)

17100421188788140168…24087056590720464001

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

3.420 × 10⁹⁸(99-digit number)

34200842377576280336…48174113181440927999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.420 × 10⁹⁸(99-digit number)

34200842377576280336…48174113181440928001

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

6.840 × 10⁹⁸(99-digit number)

68401684755152560672…96348226362881855999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.840 × 10⁹⁸(99-digit number)

68401684755152560672…96348226362881856001

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

1.368 × 10⁹⁹(100-digit number)

13680336951030512134…92696452725763711999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.368 × 10⁹⁹(100-digit number)

13680336951030512134…92696452725763712001

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