Block #444,090

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 12:55:59 AM · Difficulty 10.3426 · 6,355,164 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91091ff11b9a8f3d3f0e09452f14a8ccc23ac8fad3429f4497b8347ef1011e91

View on Chainz ↗

Height

#444,090

Difficulty

10.342565

Transactions

Size

889 B

Version

Bits

0a57b257

Nonce

2,412,694,272

Timestamp

3/15/2014, 12:55:59 AM

Confirmations

6,355,164

Mined by

AdmLQqEBU14cQNNcCjBHmxcccGrW9AUmd9

Merkle Root

e3db72426c8375fb0fc56937cafcd49a71ab261b0c3d7564c00a75298b046b03

Transactions (3)

Coinbase8626b1415f4032…3dcfb4f1e7db5e

1 in → 1 out9.3500 XPM89 B

AdmLQqEB…rW9AUmd9

3874e812caf0b3…3031c79221d51c

2 in → 7 out18.6700 XPM477 B

AeKNrjNj…1NEq95Ta AbhQSvKj…dxchi84d AeTeGX3T…2Nm2Fveq AT84m5QM…XEF1yxxC AWpvCBBf…yE35vgWj

e85d4dddb25b0d…9c8a7eb07e245a

1 in → 2 out3.1720 XPM227 B

AbMH1CXh…4CZZ7jJJ AQKPqiKp…F3DH3w1E

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.

1.951 × 10¹⁰⁹(110-digit number)

19513427093426553309…69011819685476270079

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

1.951 × 10¹⁰⁹(110-digit number)

19513427093426553309…69011819685476270079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.951 × 10¹⁰⁹(110-digit number)

19513427093426553309…69011819685476270081

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

3.902 × 10¹⁰⁹(110-digit number)

39026854186853106619…38023639370952540159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.902 × 10¹⁰⁹(110-digit number)

39026854186853106619…38023639370952540161

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

7.805 × 10¹⁰⁹(110-digit number)

78053708373706213238…76047278741905080319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.805 × 10¹⁰⁹(110-digit number)

78053708373706213238…76047278741905080321

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

1.561 × 10¹¹⁰(111-digit number)

15610741674741242647…52094557483810160639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.561 × 10¹¹⁰(111-digit number)

15610741674741242647…52094557483810160641

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

3.122 × 10¹¹⁰(111-digit number)

31221483349482485295…04189114967620321279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.122 × 10¹¹⁰(111-digit number)

31221483349482485295…04189114967620321281

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