Block #445,189

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 5:26:27 PM · Difficulty 10.3557 · 6,361,907 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6802756174c48818ff365ccce95e984e41ed06ce97a8dbb5c2df05ee6fcf7f8c

View on Chainz ↗

Height

#445,189

Difficulty

10.355694

Transactions

Size

1.52 KB

Version

Bits

0a5b0ec8

Nonce

292,585

Timestamp

3/15/2014, 5:26:27 PM

Confirmations

6,361,907

Mined by

⛏️ aS${AMHMrUuKAvovGoqqi8yFG5hR88jgEj6HLr

Merkle Root

6887fce3ad67f53500a0c025ac59e2faf9a81411ccc62977fe7dc43ebdebfbcc

Transactions (2)

Coinbaseeb3b349903c89c…f14d76f224e7b4

1 in → 21 out9.3100 XPM777 B

AMHMrUuK…jgEj6HLr AQvZBsUo…hppgRZTJ ARck9uUe…jQe3uJMp AJLB8H7s…MRD4s5wA AGKhfQo2…h7fBXLX6

dfa52ee4a07412…33c671b5915261

3 in → 10 out27.9500 XPM691 B

AR5Go142…BMWwEYuG AeKNrjNj…1NEq95Ta AGXK7b8o…SukAF8rV AJGng3Vu…HfiEdb5C APd3tden…qhRE2ARG

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.

3.705 × 10⁹⁹(100-digit number)

37055512282179439107…41112255195261302239

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

3.705 × 10⁹⁹(100-digit number)

37055512282179439107…41112255195261302239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.705 × 10⁹⁹(100-digit number)

37055512282179439107…41112255195261302241

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

7.411 × 10⁹⁹(100-digit number)

74111024564358878214…82224510390522604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.411 × 10⁹⁹(100-digit number)

74111024564358878214…82224510390522604481

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

1.482 × 10¹⁰⁰(101-digit number)

14822204912871775642…64449020781045208959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.482 × 10¹⁰⁰(101-digit number)

14822204912871775642…64449020781045208961

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

2.964 × 10¹⁰⁰(101-digit number)

29644409825743551285…28898041562090417919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.964 × 10¹⁰⁰(101-digit number)

29644409825743551285…28898041562090417921

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

5.928 × 10¹⁰⁰(101-digit number)

59288819651487102571…57796083124180835839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.928 × 10¹⁰⁰(101-digit number)

59288819651487102571…57796083124180835841

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 #445,189

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