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Block #41,688

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 5:06:09 PM · Difficulty 8.5451 · 6,748,175 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1dcd9bbd3c60677048cef4b3653df8b4fd94f52b3982aac822afc5a6f7f49f67

View on Chainz ↗

Height

#41,688

Difficulty

8.545132

Transactions

Size

198 B

Version

Bits

088b8dc4

Nonce

480

Timestamp

7/14/2013, 5:06:09 PM

Confirmations

6,748,175

Merkle Root

c8d4e7624bcf5139ce7e942827a466f6c1293b2ecc0e02e18b1dbef519c44d98

Transactions (1)

Coinbasec8d4e7624bcf51…1dbef519c44d98

1 in → 1 out13.6800 XPM110 B

APf72TCv…gY6GqxZn

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.

4.634 × 10⁸⁸(89-digit number)

46347619306901084477…98109890364508029600

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

4.634 × 10⁸⁸(89-digit number)

46347619306901084477…98109890364508029599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.634 × 10⁸⁸(89-digit number)

46347619306901084477…98109890364508029601

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

9.269 × 10⁸⁸(89-digit number)

92695238613802168954…96219780729016059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.269 × 10⁸⁸(89-digit number)

92695238613802168954…96219780729016059201

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

1.853 × 10⁸⁹(90-digit number)

18539047722760433790…92439561458032118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.853 × 10⁸⁹(90-digit number)

18539047722760433790…92439561458032118401

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

3.707 × 10⁸⁹(90-digit number)

37078095445520867581…84879122916064236799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.707 × 10⁸⁹(90-digit number)

37078095445520867581…84879122916064236801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 41688

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 1dcd9bbd3c60677048cef4b3653df8b4fd94f52b3982aac822afc5a6f7f49f67

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 #41,688 on Chainz ↗