Home/Chain Registry/Block #87,418

Block #87,418

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/28/2013, 9:26:45 PM · Difficulty 9.2760 · 6,707,159 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a653172aacc9edc123252bccb96838bfb79fad0bcad0851c0609966714cbfb3

View on Chainz ↗

Height

#87,418

Difficulty

9.275965

Transactions

Size

2.10 KB

Version

Bits

0946a5a2

Nonce

86,404

Timestamp

7/28/2013, 9:26:45 PM

Confirmations

6,707,159

Merkle Root

2717fce66dbf64666a3a25a169c12493637a6140f0ce8ae67f5b56c3a2cf4841

Transactions (3)

Coinbase58beb46240d1f6…57299f92bc7f83

1 in → 1 out11.6400 XPM109 B

AXDpUdKf…6wezXPqZ

d1e6e80fc50694…3dc65a914b2869

5 in → 1 out61.3400 XPM616 B

AQAph9Ee…Bh4omZLF

9fa841f484012c…cb8e4b61bdb458

11 in → 2 out127.7400 XPM1.30 KB

AUckWJ4d…rccphzch AJc7ETo3…y5s7mhvH

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.

4.729 × 10¹¹¹(112-digit number)

47292525994822624349…90604769331502123610

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

4.729 × 10¹¹¹(112-digit number)

47292525994822624349…90604769331502123609

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.729 × 10¹¹¹(112-digit number)

47292525994822624349…90604769331502123611

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

9.458 × 10¹¹¹(112-digit number)

94585051989645248699…81209538663004247219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.458 × 10¹¹¹(112-digit number)

94585051989645248699…81209538663004247221

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

1.891 × 10¹¹²(113-digit number)

18917010397929049739…62419077326008494439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.891 × 10¹¹²(113-digit number)

18917010397929049739…62419077326008494441

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

3.783 × 10¹¹²(113-digit number)

37834020795858099479…24838154652016988879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.783 × 10¹¹²(113-digit number)

37834020795858099479…24838154652016988881

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

7.566 × 10¹¹²(113-digit number)

75668041591716198959…49676309304033977759

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 87418

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 2a653172aacc9edc123252bccb96838bfb79fad0bcad0851c0609966714cbfb3

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 #87,418 on Chainz ↗