Block #230,774

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 12:43:42 AM · Difficulty 9.9399 · 6,560,884 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85ce623a9b38df8d1c492c4363e67d1cd04a82d90fb39df2ae1e0818918daa86

View on Chainz ↗

Height

#230,774

Difficulty

9.939902

Transactions

Size

1.22 KB

Version

Bits

09f09d72

Nonce

71,142

Timestamp

10/28/2013, 12:43:42 AM

Confirmations

6,560,884

Merkle Root

674ef8616fd0706158a7bf5efed6e35df2de4161abb994ec03e00c35d366e5ce

Transactions (3)

Coinbase26191943e3c53c…e495ac4c9b23a9

1 in → 1 out10.1300 XPM109 B

AWscwrCf…NvepQkLX

cca85b73440c24…d0962723a3b203

5 in → 2 out159.0911 XPM820 B

Ad93iDkL…JStUv8zS AXXD9rC2…Vb5reFe7

b1a95329c663db…05513a89340d1f

1 in → 2 out6.0490 XPM227 B

AMY5iKG8…NbdFoZVx Ab3dSvM7…Qoxxb9tp

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.

9.691 × 10⁹⁴(95-digit number)

96919708000909493551…84913768774737128959

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

9.691 × 10⁹⁴(95-digit number)

96919708000909493551…84913768774737128959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.691 × 10⁹⁴(95-digit number)

96919708000909493551…84913768774737128961

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

1.938 × 10⁹⁵(96-digit number)

19383941600181898710…69827537549474257919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.938 × 10⁹⁵(96-digit number)

19383941600181898710…69827537549474257921

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

3.876 × 10⁹⁵(96-digit number)

38767883200363797420…39655075098948515839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.876 × 10⁹⁵(96-digit number)

38767883200363797420…39655075098948515841

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

7.753 × 10⁹⁵(96-digit number)

77535766400727594841…79310150197897031679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.753 × 10⁹⁵(96-digit number)

77535766400727594841…79310150197897031681

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

1.550 × 10⁹⁶(97-digit number)

15507153280145518968…58620300395794063359

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