Block #439,416

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 4:23:41 PM · Difficulty 10.3596 · 6,370,086 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60a8f61478d173118f76f0898be8c6900f7fad58242627f7a757d3c09c50c96f

View on Chainz ↗

Height

#439,416

Difficulty

10.359604

Transactions

Size

1.70 KB

Version

Bits

0a5c0f08

Nonce

52,456

Timestamp

3/11/2014, 4:23:41 PM

Confirmations

6,370,086

Mined by

⛏️ xAEAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

16ccf4d5eda72a9249a854b4ce4ffcdae75aeefc0e6e78ec308db027f573a10b

Transactions (5)

Coinbase700e6bd83e289e…d79856bcfd06b9

1 in → 20 out9.3400 XPM743 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH AcgDwGo8…BBFwbjVo ASgUri65…C7NLcyBg

f93be837a2175a…747126ac8e5ae8

1 in → 2 out5.4782 XPM227 B

AMwbtPwq…wQHQbL3o ATfFpSTq…V5tFWL1z

adc952705957c2…236c725c235359

1 in → 2 out1.1698 XPM225 B

Ab7KvdoN…BMF3E7hn AKrefzxL…2esESKzR

0f7b0ea4bf9087…72943f79bbdd2b

1 in → 2 out4.1775 XPM226 B

AVKgdMue…rrwmdQma AQhcphJM…64SK6uYL

76c7ecd533094f…1af0e046f89dd8

1 in → 2 out4.4867 XPM227 B

ALGKwvEa…MEncvtXn AL6ykfNj…MdVCqsVL

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.

1.725 × 10⁹⁹(100-digit number)

17251208178910712169…72168135365822003199

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

1.725 × 10⁹⁹(100-digit number)

17251208178910712169…72168135365822003199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.725 × 10⁹⁹(100-digit number)

17251208178910712169…72168135365822003201

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

3.450 × 10⁹⁹(100-digit number)

34502416357821424339…44336270731644006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.450 × 10⁹⁹(100-digit number)

34502416357821424339…44336270731644006401

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

6.900 × 10⁹⁹(100-digit number)

69004832715642848679…88672541463288012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.900 × 10⁹⁹(100-digit number)

69004832715642848679…88672541463288012801

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

1.380 × 10¹⁰⁰(101-digit number)

13800966543128569735…77345082926576025599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.380 × 10¹⁰⁰(101-digit number)

13800966543128569735…77345082926576025601

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

2.760 × 10¹⁰⁰(101-digit number)

27601933086257139471…54690165853152051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.760 × 10¹⁰⁰(101-digit number)

27601933086257139471…54690165853152051201

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 #439,416

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