Block #195,012

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 12:23:27 PM · Difficulty 9.8803 · 6,612,908 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5493a1d22fd4f3c4e252a3309c328d993c13dddcacfd05a678f90998bdf4951

View on Chainz ↗

Height

#195,012

Difficulty

9.880296

Transactions

Size

3.77 KB

Version

Bits

09e15b12

Nonce

1,164,738,186

Timestamp

10/5/2013, 12:23:27 PM

Confirmations

6,612,908

Mined by

⛏️ RPAJNMkswRnv53DzxPCm9rAQZYrkSnXAFUHL

Merkle Root

c8fc169a908842e39edeafd2c4a5e5bd151fe7e5c09a5df02dbb652df1d5e962

Transactions (1)

Coinbasec8fc169a908842…bb652df1d5e962

1 in → 109 out10.1900 XPM3.68 KB

AJNMkswR…SnXAFUHL ALWSkoC4…zeCoyaty ATq9gtso…RsTyRxat AR7hUyNW…iuooRCti AZXoSj9g…CHwewozP

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.

4.995 × 10⁹⁴(95-digit number)

49957091390097372593…13243034180330414079

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

4.995 × 10⁹⁴(95-digit number)

49957091390097372593…13243034180330414079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.995 × 10⁹⁴(95-digit number)

49957091390097372593…13243034180330414081

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

9.991 × 10⁹⁴(95-digit number)

99914182780194745187…26486068360660828159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.991 × 10⁹⁴(95-digit number)

99914182780194745187…26486068360660828161

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

1.998 × 10⁹⁵(96-digit number)

19982836556038949037…52972136721321656319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.998 × 10⁹⁵(96-digit number)

19982836556038949037…52972136721321656321

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

3.996 × 10⁹⁵(96-digit number)

39965673112077898074…05944273442643312639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.996 × 10⁹⁵(96-digit number)

39965673112077898074…05944273442643312641

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

7.993 × 10⁹⁵(96-digit number)

79931346224155796149…11888546885286625279

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 #195,012

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