Block #431,593

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 8:03:00 AM · Difficulty 10.3394 · 6,385,708 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00da3f3c3efa10ddf1680e21795b6866de3100d779796f07884f7c784d88e0ba

View on Chainz ↗

Height

#431,593

Difficulty

10.339445

Transactions

Size

2.25 KB

Version

Bits

0a56e5d7

Nonce

24,455

Timestamp

3/6/2014, 8:03:00 AM

Confirmations

6,385,708

Mined by

⛏️ P2SHALXdYvwStnYULAHdepA5x1UR3jN8jP6yAR

Merkle Root

c52c2c17ba07f4ace6a13974a5d899adc15c1de6c30d61c358781002cc4ca9d8

Transactions (3)

Coinbase5d60ee4f3c439a…072f2740938ddf

1 in → 1 out9.3700 XPM111 B

ALXdYvwS…N8jP6yAR

cc37aa077b2b3d…db5d23cf3e5dc2

8 in → 2 out15.8318 XPM1.23 KB

ASQTCpT6…ENnorTuW ATxcuMs6…JmCq2rgH

ad17bcde1194b3…9ad6596a899dde

4 in → 7 out11.0998 XPM842 B

AVVCaHhW…oC78X3RW AZAYcqyP…Bf5uQ6gQ AGxYGYHa…FRp3G4Gh AVvBfWAv…s7d3svTc AL5EWFRt…kepzfkeN

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.

3.190 × 10¹⁰⁰(101-digit number)

31904890830399874739…49623883043398201439

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

3.190 × 10¹⁰⁰(101-digit number)

31904890830399874739…49623883043398201439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.190 × 10¹⁰⁰(101-digit number)

31904890830399874739…49623883043398201441

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

6.380 × 10¹⁰⁰(101-digit number)

63809781660799749479…99247766086796402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.380 × 10¹⁰⁰(101-digit number)

63809781660799749479…99247766086796402881

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

1.276 × 10¹⁰¹(102-digit number)

12761956332159949895…98495532173592805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.276 × 10¹⁰¹(102-digit number)

12761956332159949895…98495532173592805761

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

2.552 × 10¹⁰¹(102-digit number)

25523912664319899791…96991064347185611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.552 × 10¹⁰¹(102-digit number)

25523912664319899791…96991064347185611521

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

5.104 × 10¹⁰¹(102-digit number)

51047825328639799583…93982128694371223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.104 × 10¹⁰¹(102-digit number)

51047825328639799583…93982128694371223041

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 #431,593

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