Block #442,411

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 7:47:50 PM · Difficulty 10.3497 · 6,365,799 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc7f06f4f5cd8626c2cf1d801d0b13e98fc0338e387bd90a6523c130735a2015

View on Chainz ↗

Height

#442,411

Difficulty

10.349690

Transactions

Size

1.17 KB

Version

Bits

0a598544

Nonce

77,075

Timestamp

3/13/2014, 7:47:50 PM

Confirmations

6,365,799

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

dcfdc0e662b5f2d91f20f7bf76b0da488d4a0d6b33af3a6b857f019b2ed5c817

Transactions (2)

Coinbase9b79da01e10ecb…c355417a58d711

1 in → 1 out9.3400 XPM116 B

AbwWkWZt…kawDhufa

11825e227e814c…004f7ae44e4157

5 in → 10 out28.5804 XPM990 B

APoKMzcp…Qt5k4Vex AND9bh7f…Vq85QSAN AThucpHS…u81AqEsr ASu16mM2…HMZ4nzyA AL7194fk…YNQBVjTB

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.

6.170 × 10¹⁰⁴(105-digit number)

61705583489271366375…57976567256230113039

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

6.170 × 10¹⁰⁴(105-digit number)

61705583489271366375…57976567256230113039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.170 × 10¹⁰⁴(105-digit number)

61705583489271366375…57976567256230113041

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

1.234 × 10¹⁰⁵(106-digit number)

12341116697854273275…15953134512460226079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.234 × 10¹⁰⁵(106-digit number)

12341116697854273275…15953134512460226081

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

2.468 × 10¹⁰⁵(106-digit number)

24682233395708546550…31906269024920452159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.468 × 10¹⁰⁵(106-digit number)

24682233395708546550…31906269024920452161

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

4.936 × 10¹⁰⁵(106-digit number)

49364466791417093100…63812538049840904319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.936 × 10¹⁰⁵(106-digit number)

49364466791417093100…63812538049840904321

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

9.872 × 10¹⁰⁵(106-digit number)

98728933582834186200…27625076099681808639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.872 × 10¹⁰⁵(106-digit number)

98728933582834186200…27625076099681808641

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 #442,411

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