Block #463,017

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 7:38:00 PM · Difficulty 10.4189 · 6,338,318 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

41b83e77ecaa2dac8557685733dfe7d4127c5bcb022beb6d58140afd7e6169dc

View on Chainz ↗

Height

#463,017

Difficulty

10.418851

Transactions

Size

1.13 KB

Version

Bits

0a6b39d0

Nonce

4,035

Timestamp

3/27/2014, 7:38:00 PM

Confirmations

6,338,318

Mined by

⛏️ aS4}AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

34ce21310b90c1135d5cea66790897e6c82b5386d36b522a0211cffd3760de04

Transactions (2)

Coinbase4d24037444491a…4046363032f951

1 in → 23 out9.2000 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn

266505adabc374…a5bdbab1e23dba

1 in → 2 out0.4924 XPM226 B

AKQtnjU2…zeVZDv8d AHK12ksm…bb2sBPaA

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.

1.053 × 10⁹⁶(97-digit number)

10536024361116417523…44399932056594513839

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

1.053 × 10⁹⁶(97-digit number)

10536024361116417523…44399932056594513839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.053 × 10⁹⁶(97-digit number)

10536024361116417523…44399932056594513841

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

2.107 × 10⁹⁶(97-digit number)

21072048722232835047…88799864113189027679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.107 × 10⁹⁶(97-digit number)

21072048722232835047…88799864113189027681

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

4.214 × 10⁹⁶(97-digit number)

42144097444465670095…77599728226378055359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.214 × 10⁹⁶(97-digit number)

42144097444465670095…77599728226378055361

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

8.428 × 10⁹⁶(97-digit number)

84288194888931340191…55199456452756110719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.428 × 10⁹⁶(97-digit number)

84288194888931340191…55199456452756110721

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

1.685 × 10⁹⁷(98-digit number)

16857638977786268038…10398912905512221439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.685 × 10⁹⁷(98-digit number)

16857638977786268038…10398912905512221441

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