Block #119,305

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/16/2013, 9:38:10 AM · Difficulty 9.7493 · 6,674,939 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f0d5fb5e393b3b3f66e4f94484237fc37d7cbf226068433cc47ddc95a278a49

View on Chainz ↗

Height

#119,305

Difficulty

9.749331

Transactions

Size

426 B

Version

Bits

09bfd425

Nonce

178,880

Timestamp

8/16/2013, 9:38:10 AM

Confirmations

6,674,939

Merkle Root

2917e995632a8a2334f15828b9045873029e0c8e9d4522b99084f8f7c263f4d5

Transactions (2)

Coinbasec8c5f559e9a8d9…6d8b7a03b7e5a4

1 in → 1 out10.5200 XPM109 B

AVTdASf7…wQZLqRtu

bc4422f0fa9109…3915fbf909519c

1 in → 2 out3168.9900 XPM226 B

AdNeXXkk…QpfXAns4 ASrsUGtr…BuKQpQ2X

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.

3.981 × 10⁹⁶(97-digit number)

39810202398319295862…82046706817924618159

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

3.981 × 10⁹⁶(97-digit number)

39810202398319295862…82046706817924618159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.981 × 10⁹⁶(97-digit number)

39810202398319295862…82046706817924618161

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

7.962 × 10⁹⁶(97-digit number)

79620404796638591724…64093413635849236319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.962 × 10⁹⁶(97-digit number)

79620404796638591724…64093413635849236321

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

1.592 × 10⁹⁷(98-digit number)

15924080959327718344…28186827271698472639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.592 × 10⁹⁷(98-digit number)

15924080959327718344…28186827271698472641

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

3.184 × 10⁹⁷(98-digit number)

31848161918655436689…56373654543396945279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.184 × 10⁹⁷(98-digit number)

31848161918655436689…56373654543396945281

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

6.369 × 10⁹⁷(98-digit number)

63696323837310873379…12747309086793890559

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