Block #463,996

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 12:31:18 PM · Difficulty 10.4152 · 6,342,910 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa136092c5f5fcd83192ddaf7f4eade23d8413e9b0af26b7d3a6c5202fc05cdc

View on Chainz ↗

Height

#463,996

Difficulty

10.415192

Transactions

Size

1.36 KB

Version

Bits

0a6a4a01

Nonce

48,710

Timestamp

3/28/2014, 12:31:18 PM

Confirmations

6,342,910

Mined by

⛏️ P2SHAdNPazA9622ZHPU99VRGwpjxTKXAGC72gB

Merkle Root

61605da09d7abecb386047f9f30f9f539a29f8884d3ee540d1f467eb616addcd

Transactions (3)

Coinbase9a140e475209f2…d87971d1c18afc

1 in → 1 out9.2200 XPM111 B

AdNPazA9…XAGC72gB

7fd45ddd20f521…28e00b12a7a57c

6 in → 2 out6.1240 XPM965 B

ARFQQyKm…2wKsHKnG AVXY4yKK…ktbuA1w9

fb26f7eb81889e…75ddfffebdd362

1 in → 2 out5.4574 XPM227 B

AGtz78Hk…YyoUHCrZ ATnvn2Nn…76es5TS5

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.

5.665 × 10⁹⁶(97-digit number)

56657428417496272048…00618767239602069759

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

5.665 × 10⁹⁶(97-digit number)

56657428417496272048…00618767239602069759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.665 × 10⁹⁶(97-digit number)

56657428417496272048…00618767239602069761

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

1.133 × 10⁹⁷(98-digit number)

11331485683499254409…01237534479204139519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.133 × 10⁹⁷(98-digit number)

11331485683499254409…01237534479204139521

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

2.266 × 10⁹⁷(98-digit number)

22662971366998508819…02475068958408279039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.266 × 10⁹⁷(98-digit number)

22662971366998508819…02475068958408279041

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

4.532 × 10⁹⁷(98-digit number)

45325942733997017638…04950137916816558079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.532 × 10⁹⁷(98-digit number)

45325942733997017638…04950137916816558081

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

9.065 × 10⁹⁷(98-digit number)

90651885467994035276…09900275833633116159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.065 × 10⁹⁷(98-digit number)

90651885467994035276…09900275833633116161

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 #463,996

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