Block #232,085

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 9:13:22 PM · Difficulty 9.9409 · 6,559,020 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78f76309d2e7f9ffdbb38510d4fbebfca0c4860550f5f333c00aa0711293f5d3

View on Chainz ↗

Height

#232,085

Difficulty

9.940935

Transactions

Size

945 B

Version

Bits

09f0e11a

Nonce

33,109

Timestamp

10/28/2013, 9:13:22 PM

Confirmations

6,559,020

Merkle Root

06a640f6a68d8573574babaf9959182f5cff1fd7bfc2f4d443c17ab1e90bd2b8

Transactions (3)

Coinbase5acdaff8ecff68…56be36655da23e

1 in → 1 out10.1200 XPM109 B

AH326Z3s…SLBApGax

d10cac5403486c…c4de0a714bc5b8

1 in → 2 out8.8654 XPM225 B

AHTAmZSG…FQGXE3Uz ASnSjgQg…fewAaNPL

6c09cbcedfe10c…b6fba2a14fe0d3

3 in → 2 out5.0596 XPM522 B

AVjaBwzf…22o3JtpX AKWqSM85…W98Gvpo5

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.

9.647 × 10⁹²(93-digit number)

96475303184946562294…50293947480884471039

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

9.647 × 10⁹²(93-digit number)

96475303184946562294…50293947480884471039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.647 × 10⁹²(93-digit number)

96475303184946562294…50293947480884471041

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

1.929 × 10⁹³(94-digit number)

19295060636989312458…00587894961768942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.929 × 10⁹³(94-digit number)

19295060636989312458…00587894961768942081

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

3.859 × 10⁹³(94-digit number)

38590121273978624917…01175789923537884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.859 × 10⁹³(94-digit number)

38590121273978624917…01175789923537884161

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

7.718 × 10⁹³(94-digit number)

77180242547957249835…02351579847075768319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.718 × 10⁹³(94-digit number)

77180242547957249835…02351579847075768321

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

1.543 × 10⁹⁴(95-digit number)

15436048509591449967…04703159694151536639

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