Block #444,360

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 5:26:09 AM · Difficulty 10.3425 · 6,347,225 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

156b51e0640e41e61c94d7969819638f957a4d707b381c080253d1a85524a9a6

View on Chainz ↗

Height

#444,360

Difficulty

10.342492

Transactions

Size

1.32 KB

Version

Bits

0a57ad89

Nonce

24,139

Timestamp

3/15/2014, 5:26:09 AM

Confirmations

6,347,225

Merkle Root

1053710f6791673e83fed2d63a6ddb042015c8144cbea68bc163494ce1404eff

Transactions (3)

Coinbased1e1515fcbb2f2…462345026693bd

1 in → 1 out9.3500 XPM110 B

AeKNrjNj…1NEq95Ta

e283cb292e6b53…b98047d34c679f

5 in → 8 out22.4179 XPM956 B

Abfxu9pR…KmBFxFwg AQYQT37a…woJiw19q AbABGh95…BpJH6dHp AeKNrjNj…1NEq95Ta AXy8CJrT…rHLoyh3A

3dba1e04718708…107caa2492894b

1 in → 1 out2.9912 XPM192 B

AX9Hnjm8…UuqJSRmE

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.

7.802 × 10¹⁰⁰(101-digit number)

78029831114067460570…82503947159671076799

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

7.802 × 10¹⁰⁰(101-digit number)

78029831114067460570…82503947159671076799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.802 × 10¹⁰⁰(101-digit number)

78029831114067460570…82503947159671076801

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

1.560 × 10¹⁰¹(102-digit number)

15605966222813492114…65007894319342153599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.560 × 10¹⁰¹(102-digit number)

15605966222813492114…65007894319342153601

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

3.121 × 10¹⁰¹(102-digit number)

31211932445626984228…30015788638684307199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.121 × 10¹⁰¹(102-digit number)

31211932445626984228…30015788638684307201

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

6.242 × 10¹⁰¹(102-digit number)

62423864891253968456…60031577277368614399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.242 × 10¹⁰¹(102-digit number)

62423864891253968456…60031577277368614401

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

1.248 × 10¹⁰²(103-digit number)

12484772978250793691…20063154554737228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.248 × 10¹⁰²(103-digit number)

12484772978250793691…20063154554737228801

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