Home/Chain Registry/Block #131,875

Block #131,875

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/24/2013, 2:01:55 PM · Difficulty 9.7860 · 6,661,130 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd8c71807a8a0faa65b4e734510bf99a94bf31db9a6091f4c01383962132ba07

View on Chainz ↗

Height

#131,875

Difficulty

9.786050

Transactions

Size

203 B

Version

Bits

09c93a8b

Nonce

6,131

Timestamp

8/24/2013, 2:01:55 PM

Confirmations

6,661,130

Merkle Root

8b9dcf875a16bd5c80ab7a2a7f0b6b8970704d23be4e1dedaaf2076a47026ae5

Transactions (1)

Coinbase8b9dcf875a16bd…f2076a47026ae5

1 in → 1 out10.4300 XPM112 B

AT5A2KL6…CT16n6i2

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.

4.580 × 10⁹⁶(97-digit number)

45805061332941520126…19105615350478218880

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

4.580 × 10⁹⁶(97-digit number)

45805061332941520126…19105615350478218879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.580 × 10⁹⁶(97-digit number)

45805061332941520126…19105615350478218881

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

9.161 × 10⁹⁶(97-digit number)

91610122665883040252…38211230700956437759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.161 × 10⁹⁶(97-digit number)

91610122665883040252…38211230700956437761

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

1.832 × 10⁹⁷(98-digit number)

18322024533176608050…76422461401912875519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.832 × 10⁹⁷(98-digit number)

18322024533176608050…76422461401912875521

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

3.664 × 10⁹⁷(98-digit number)

36644049066353216100…52844922803825751039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.664 × 10⁹⁷(98-digit number)

36644049066353216100…52844922803825751041

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

7.328 × 10⁹⁷(98-digit number)

73288098132706432201…05689845607651502079

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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 131875

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock fd8c71807a8a0faa65b4e734510bf99a94bf31db9a6091f4c01383962132ba07

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #131,875 on Chainz ↗