Block #231,135

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 6:08:55 AM · Difficulty 9.9404 · 6,578,676 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

130a567bb6b883c3f4d0f833ae4ded89d4b46f32a3c200fed1fcfe639996b81b

View on Chainz ↗

Height

#231,135

Difficulty

9.940356

Transactions

Size

1.94 KB

Version

Bits

09f0bb2f

Nonce

176,755

Timestamp

10/28/2013, 6:08:55 AM

Confirmations

6,578,676

Mined by

⛏️ RmANwfg8TXkwi9u7KLeGy6rPtZNjn1YQhihe

Merkle Root

4d71ac02421d034af69ff62e29d3036f115fde94e5f7c47b3a30f2a4036021e4

Transactions (1)

Coinbase4d71ac02421d03…30f2a4036021e4

1 in → 54 out10.0900 XPM1.85 KB

ANwfg8TX…n1YQhihe AeEcSGAf…HjtsPDKX AMVsYFfp…DB9jn4fb ALFWpHxd…zhX7LjhL AUmqvzVP…R7Pd9B3z

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.

2.450 × 10⁹⁴(95-digit number)

24508118352264805448…06674328479042944549

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

2.450 × 10⁹⁴(95-digit number)

24508118352264805448…06674328479042944549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.450 × 10⁹⁴(95-digit number)

24508118352264805448…06674328479042944551

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

4.901 × 10⁹⁴(95-digit number)

49016236704529610896…13348656958085889099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.901 × 10⁹⁴(95-digit number)

49016236704529610896…13348656958085889101

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

9.803 × 10⁹⁴(95-digit number)

98032473409059221792…26697313916171778199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.803 × 10⁹⁴(95-digit number)

98032473409059221792…26697313916171778201

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

1.960 × 10⁹⁵(96-digit number)

19606494681811844358…53394627832343556399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.960 × 10⁹⁵(96-digit number)

19606494681811844358…53394627832343556401

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

3.921 × 10⁹⁵(96-digit number)

39212989363623688717…06789255664687112799

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 #231,135

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