Block #450,667

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/19/2014, 10:40:39 AM · Difficulty 10.3749 · 6,363,632 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d909c5e4acbf1bef121e87cd4922a4b157da76e5a7d94e03ef48788ea7ff08e

View on Chainz ↗

Height

#450,667

Difficulty

10.374891

Transactions

Size

3.32 KB

Version

Bits

0a5ff8de

Nonce

4,200

Timestamp

3/19/2014, 10:40:39 AM

Confirmations

6,363,632

Mined by

⛏️ kaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

aef340a2cf23962e148118787f2a2ea7283f6f10485135111bc2e94178b65f36

Transactions (2)

Coinbase7136982c0e1996…a7e865f7cfcf78

1 in → 25 out9.2800 XPM913 B

AQvZBsUo…hppgRZTJ AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AWMrD5hP…ZwsoxvZ3 ALqxX1WA…hsKjbnXn

5986ba4a23479b…17bdc78985cf68

9 in → 31 out56.3491 XPM2.34 KB

AUkdqaxr…4jcbMUQ7 ALfudnmA…NLfAUkf3 ALXa1oKc…rwjzvEVp AYxRMkrV…4xUzBCzM AdFpJ3iR…YmjR9m1d

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.

2.667 × 10¹⁰¹(102-digit number)

26672992467244685469…52859209448548556799

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

2.667 × 10¹⁰¹(102-digit number)

26672992467244685469…52859209448548556799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.667 × 10¹⁰¹(102-digit number)

26672992467244685469…52859209448548556801

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

5.334 × 10¹⁰¹(102-digit number)

53345984934489370938…05718418897097113599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.334 × 10¹⁰¹(102-digit number)

53345984934489370938…05718418897097113601

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

1.066 × 10¹⁰²(103-digit number)

10669196986897874187…11436837794194227199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.066 × 10¹⁰²(103-digit number)

10669196986897874187…11436837794194227201

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

2.133 × 10¹⁰²(103-digit number)

21338393973795748375…22873675588388454399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.133 × 10¹⁰²(103-digit number)

21338393973795748375…22873675588388454401

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

4.267 × 10¹⁰²(103-digit number)

42676787947591496750…45747351176776908799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.267 × 10¹⁰²(103-digit number)

42676787947591496750…45747351176776908801

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 #450,667

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