Block #263,711

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/18/2013, 1:48:43 AM · Difficulty 9.9656 · 6,552,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

411b2ac18c3f9db5623c93c10e2855e315ce94124e3ca35144dfc307f9e7d344

View on Chainz ↗

Height

#263,711

Difficulty

9.965589

Transactions

Size

1.75 KB

Version

Bits

09f730dc

Nonce

7,710

Timestamp

11/18/2013, 1:48:43 AM

Confirmations

6,552,417

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

f9ab4bbaf194831cb9006e36e06aeb460e12be6b94ea129807f79ee978892580

Transactions (4)

Coinbasefe7ffb9362702e…8dca4207ff7e53

1 in → 2 out10.0800 XPM137 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

aef75a1e6611bd…fbe2506453820a

4 in → 2 out168.9100 XPM672 B

ATWUZnMW…V5iJvMva AcRRwhBA…tmjc6bV9

a8eccff48cccf9…8b952a045b03c6

3 in → 2 out200.0130 XPM521 B

AKRNwy9r…gamBuurg Aa2WJj29…SpcBSai5

94c3dcca71eb09…db408a16941d6d

2 in → 2 out7.6100 XPM373 B

AW4wuyvX…Sz17rnFN ALyzHQDz…ig9Upy2K

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.

8.058 × 10⁹³(94-digit number)

80582151682997982816…45616080393696078539

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

8.058 × 10⁹³(94-digit number)

80582151682997982816…45616080393696078539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.058 × 10⁹³(94-digit number)

80582151682997982816…45616080393696078541

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

1.611 × 10⁹⁴(95-digit number)

16116430336599596563…91232160787392157079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.611 × 10⁹⁴(95-digit number)

16116430336599596563…91232160787392157081

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

3.223 × 10⁹⁴(95-digit number)

32232860673199193126…82464321574784314159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.223 × 10⁹⁴(95-digit number)

32232860673199193126…82464321574784314161

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

6.446 × 10⁹⁴(95-digit number)

64465721346398386253…64928643149568628319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.446 × 10⁹⁴(95-digit number)

64465721346398386253…64928643149568628321

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

1.289 × 10⁹⁵(96-digit number)

12893144269279677250…29857286299137256639

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

Block #263,711

Cookie Preferences