Block #443,472

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 2:05:51 PM · Difficulty 10.3455 · 6,363,849 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cec63ed4662090a3c53f59d7eca00e69af9aabc6c4ab19d8dc2c23faf09c1285

View on Chainz ↗

Height

#443,472

Difficulty

10.345492

Transactions

Size

9.59 KB

Version

Bits

0a58722f

Nonce

1,793

Timestamp

3/14/2014, 2:05:51 PM

Confirmations

6,363,849

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

00fbaaf4e8262ab48dc6a5274bfb30fb5cf4ec30ae9febc3d0be81351b1b8044

Transactions (3)

Coinbase432c592c0cd86f…21869cb2f97489

1 in → 1 out9.4300 XPM116 B

AbwWkWZt…kawDhufa

b02384b518fa08…ae29c3150c01f9

58 in → 1 out58.3819 XPM8.42 KB

AKTp4LNR…Et8yJU2A

83b157622fc71f…276f0f93a61c24

5 in → 10 out28.5207 XPM987 B

ASdqdzs7…wiSJQHba AVkVLBYw…kNh65kqx AQtisFei…VwsPGKH9 AJ9HT2JV…tLekZoHB AVnfbCeS…wU5T1Pkc

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.

1.339 × 10¹⁰⁰(101-digit number)

13390496517786062984…87866033505559756799

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

1.339 × 10¹⁰⁰(101-digit number)

13390496517786062984…87866033505559756799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.339 × 10¹⁰⁰(101-digit number)

13390496517786062984…87866033505559756801

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

2.678 × 10¹⁰⁰(101-digit number)

26780993035572125969…75732067011119513599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.678 × 10¹⁰⁰(101-digit number)

26780993035572125969…75732067011119513601

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

5.356 × 10¹⁰⁰(101-digit number)

53561986071144251939…51464134022239027199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.356 × 10¹⁰⁰(101-digit number)

53561986071144251939…51464134022239027201

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

1.071 × 10¹⁰¹(102-digit number)

10712397214228850387…02928268044478054399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.071 × 10¹⁰¹(102-digit number)

10712397214228850387…02928268044478054401

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

2.142 × 10¹⁰¹(102-digit number)

21424794428457700775…05856536088956108799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.142 × 10¹⁰¹(102-digit number)

21424794428457700775…05856536088956108801

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 #443,472

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