Block #211,913

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 11:17:25 PM · Difficulty 9.9180 · 6,580,861 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79920ce8f3cd95a7bd68290c782cb0045ed3506d4d7bdd813b67201636f481c4

View on Chainz ↗

Height

#211,913

Difficulty

9.918009

Transactions

Size

1.47 KB

Version

Bits

09eb02a1

Nonce

293,372

Timestamp

10/15/2013, 11:17:25 PM

Confirmations

6,580,861

Merkle Root

6dfbfa5237b873067449516fd1938bab17b9f8d0af051cc95d94bdd66b038569

Transactions (4)

Coinbaseab6eebb706220e…e788b729097804

1 in → 1 out10.1860 XPM109 B

AWh2L9s4…99b84JcT

8829d7e63bbea0…bcd9acd2139026

3 in → 2 out300.0100 XPM520 B

AHD5a71a…SoGcf2ev ATDg1wpK…dc5kwZ3e

b8be053be1defa…f87527196d716f

2 in → 2 out20.3300 XPM304 B

AFz9fXym…wh4UqpkL ASCVFhnW…3Xcf9ixv

abee6b87a04e56…c856c9f55c8d18

3 in → 1 out6.0000 XPM486 B

AUprsALq…PjgiNTyj

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.

2.566 × 10⁹⁴(95-digit number)

25663903188684737614…84333908603633474589

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

2.566 × 10⁹⁴(95-digit number)

25663903188684737614…84333908603633474589

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.566 × 10⁹⁴(95-digit number)

25663903188684737614…84333908603633474591

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

5.132 × 10⁹⁴(95-digit number)

51327806377369475229…68667817207266949179

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.132 × 10⁹⁴(95-digit number)

51327806377369475229…68667817207266949181

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

1.026 × 10⁹⁵(96-digit number)

10265561275473895045…37335634414533898359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.026 × 10⁹⁵(96-digit number)

10265561275473895045…37335634414533898361

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

2.053 × 10⁹⁵(96-digit number)

20531122550947790091…74671268829067796719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.053 × 10⁹⁵(96-digit number)

20531122550947790091…74671268829067796721

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

4.106 × 10⁹⁵(96-digit number)

41062245101895580183…49342537658135593439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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