Block #192,058

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/3/2013, 2:34:24 PM · Difficulty 9.8748 · 6,625,874 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0f1942aba41474f8101e44858cd00c9dcddf53076dbce72be986059baada721

View on Chainz ↗

Height

#192,058

Difficulty

9.874822

Transactions

Size

1.86 KB

Version

Bits

09dff457

Nonce

183,453

Timestamp

10/3/2013, 2:34:24 PM

Confirmations

6,625,874

Mined by

⛏️ P2SHALVYxZfyofnKuymwkhc5zqKN3ZaUZAJxQ8

Merkle Root

15e5925320c180109d10f2fd8e32dd1b9ef57d134b7f2912e0d4837ddb24efcc

Transactions (2)

Coinbase0c338356b1a2fb…9cb43fcdbda2bc

1 in → 1 out10.2600 XPM109 B

ALVYxZfy…aUZAJxQ8

e55e3ea1267ac8…11bc3592174eb6

11 in → 2 out22.6343 XPM1.67 KB

AGbCrA36…VTB4h9kV AUUJC7ne…cmZaPWM6

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.

3.064 × 10⁹²(93-digit number)

30645676338025716153…09589521623133424639

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

3.064 × 10⁹²(93-digit number)

30645676338025716153…09589521623133424639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.064 × 10⁹²(93-digit number)

30645676338025716153…09589521623133424641

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

6.129 × 10⁹²(93-digit number)

61291352676051432306…19179043246266849279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.129 × 10⁹²(93-digit number)

61291352676051432306…19179043246266849281

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

1.225 × 10⁹³(94-digit number)

12258270535210286461…38358086492533698559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.225 × 10⁹³(94-digit number)

12258270535210286461…38358086492533698561

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

2.451 × 10⁹³(94-digit number)

24516541070420572922…76716172985067397119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.451 × 10⁹³(94-digit number)

24516541070420572922…76716172985067397121

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

4.903 × 10⁹³(94-digit number)

49033082140841145844…53432345970134794239

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 #192,058

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