Block #168,884

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/17/2013, 3:00:13 PM · Difficulty 9.8683 · 6,634,645 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a02b73a9a6e4986c757eeee9a22fbb9f9849431b5c1d7859300992aedd158f90

View on Chainz ↗

Height

#168,884

Difficulty

9.868266

Transactions

Size

1.81 KB

Version

Bits

09de46a9

Nonce

37,254

Timestamp

9/17/2013, 3:00:13 PM

Confirmations

6,634,645

Mined by

⛏️ P2SHAPXbZ5rTvGBKFQRz9D6GCCEGQ7tYpoKGz2

Merkle Root

12933497a4bfdfcd802c52c3dae8954e4d636596400e72cc6763fb3a8763cac4

Transactions (5)

Coinbasea1cd93effb6d3e…0811baf2bbc46c

1 in → 1 out10.2900 XPM109 B

APXbZ5rT…tYpoKGz2

6352a34865902a…03fb7a76867155

2 in → 2 out310.0556 XPM374 B

AR4jwU25…iPJokCxM AKPsK7hq…JimrEcdU

55791f79509447…435797029c4d56

4 in → 2 out21.2924 XPM603 B

ALWrH6tE…7LyMPbWP AUv3ZpeT…UrZhGUfD

62a53ed8e54757…21ccee55d49bbc

1 in → 1 out10.2900 XPM157 B

AUQWNLX2…FxwsS5kV

76e6687280418d…e500b46685dfb8

3 in → 2 out6.0472 XPM522 B

AVe2KxVJ…gPkyS6sj AKC3T67f…SeXuVXWn

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.

6.166 × 10⁹³(94-digit number)

61663329824894553411…86833292203783739839

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

6.166 × 10⁹³(94-digit number)

61663329824894553411…86833292203783739839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.166 × 10⁹³(94-digit number)

61663329824894553411…86833292203783739841

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

1.233 × 10⁹⁴(95-digit number)

12332665964978910682…73666584407567479679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.233 × 10⁹⁴(95-digit number)

12332665964978910682…73666584407567479681

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

2.466 × 10⁹⁴(95-digit number)

24665331929957821364…47333168815134959359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.466 × 10⁹⁴(95-digit number)

24665331929957821364…47333168815134959361

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

4.933 × 10⁹⁴(95-digit number)

49330663859915642729…94666337630269918719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.933 × 10⁹⁴(95-digit number)

49330663859915642729…94666337630269918721

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

9.866 × 10⁹⁴(95-digit number)

98661327719831285458…89332675260539837439

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