Block #462,370

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 9:57:29 AM · Difficulty 10.4113 · 6,347,284 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5789b5f2d8e93778771cf54b6dbbaec5a5e014401cbd0644db786e3bb40989ee

View on Chainz ↗

Height

#462,370

Difficulty

10.411316

Transactions

Size

968 B

Version

Bits

0a694bfc

Nonce

101,646

Timestamp

3/27/2014, 9:57:29 AM

Confirmations

6,347,284

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

6b207cd21596e590287f454915b175828b15844cf4dd4e4b842f8d74c27446f9

Transactions (4)

Coinbase2fb45fda21adc8…58bddd82728dc2

1 in → 4 out9.2400 XPM199 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN Aa2Amg89…4rjYrsPZ AJno7LX2…vo4wdWtY

cc32dc340469e9…3e5630e3d527ac

1 in → 2 out8.1736 XPM225 B

ATADmBFX…5jBQQUrH ALpkLdKE…92NroW64

413b960b4c1aca…6ef5468425d650

1 in → 2 out5.5665 XPM226 B

AMNoS32S…niT5aQFA AeH5jTGe…sKFctWhD

0f73afdca6604b…b36865eb6fd86e

1 in → 2 out4.4211 XPM226 B

APufLoBY…j8beDzwB ATEhhiKB…RxD17TvE

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.

5.785 × 10⁹⁸(99-digit number)

57857629150613072360…83580847403347306859

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

5.785 × 10⁹⁸(99-digit number)

57857629150613072360…83580847403347306859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.785 × 10⁹⁸(99-digit number)

57857629150613072360…83580847403347306861

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

1.157 × 10⁹⁹(100-digit number)

11571525830122614472…67161694806694613719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.157 × 10⁹⁹(100-digit number)

11571525830122614472…67161694806694613721

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

2.314 × 10⁹⁹(100-digit number)

23143051660245228944…34323389613389227439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.314 × 10⁹⁹(100-digit number)

23143051660245228944…34323389613389227441

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

4.628 × 10⁹⁹(100-digit number)

46286103320490457888…68646779226778454879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.628 × 10⁹⁹(100-digit number)

46286103320490457888…68646779226778454881

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

9.257 × 10⁹⁹(100-digit number)

92572206640980915777…37293558453556909759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.257 × 10⁹⁹(100-digit number)

92572206640980915777…37293558453556909761

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 #462,370

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