Block #461,710

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 10:05:26 PM · Difficulty 10.4155 · 6,346,543 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44e6dc786d1ab5a7633ebd58008d36f5e9a0799cf457c44292fe36639bfeb6fe

View on Chainz ↗

Height

#461,710

Difficulty

10.415477

Transactions

Size

1.83 KB

Version

Bits

0a6a5cb1

Nonce

11,123,476

Timestamp

3/26/2014, 10:05:26 PM

Confirmations

6,346,543

Mined by

⛏️ P2SHAQrtE9QShJuR6fRZkSGHZPhWP1qM4UfwtC

Merkle Root

247fdc05d9894ac76cae8827e96408cdf4f790ea1d8de7c75f07ddc58fe80570

Transactions (2)

Coinbase4d6431d377534c…978b4fa1d81adb

1 in → 1 out9.2200 XPM109 B

AQrtE9QS…qM4UfwtC

a0f600b75c2b44…c76e6a4aeee159

8 in → 21 out66.2793 XPM1.63 KB

AWwtwZZF…R3JDVm9c ARBEqonV…m5Bp67tn ANxERLYc…v7fC1vqc AXHYt6qb…r5FS5i7c AdipcxVo…qAZrfiDs

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.

1.118 × 10⁹⁷(98-digit number)

11182291071087716819…05606730831909591039

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

1.118 × 10⁹⁷(98-digit number)

11182291071087716819…05606730831909591039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.118 × 10⁹⁷(98-digit number)

11182291071087716819…05606730831909591041

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

2.236 × 10⁹⁷(98-digit number)

22364582142175433639…11213461663819182079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.236 × 10⁹⁷(98-digit number)

22364582142175433639…11213461663819182081

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

4.472 × 10⁹⁷(98-digit number)

44729164284350867279…22426923327638364159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.472 × 10⁹⁷(98-digit number)

44729164284350867279…22426923327638364161

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

8.945 × 10⁹⁷(98-digit number)

89458328568701734558…44853846655276728319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.945 × 10⁹⁷(98-digit number)

89458328568701734558…44853846655276728321

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

1.789 × 10⁹⁸(99-digit number)

17891665713740346911…89707693310553456639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.789 × 10⁹⁸(99-digit number)

17891665713740346911…89707693310553456641

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 #461,710

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