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Home/Chain Registry/Block #2,716,659

Block #2,716,659

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/22/2018, 4:30:10 PM Β· Difficulty 11.6134 Β· 4,127,028 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
6fba4510cc8ef4888207bb16e1c78f0cc71b5bb572e0c3ff182779c15fe865bf
View on Chainz β†—

Difficulty

11.613430

Transactions

1

Size

199 B

Version

2

Bits

0b9d09c3

Nonce

1,692,961,022

Timestamp

6/22/2018, 4:30:10 PM

Confirmations

4,127,028

Merkle Root

491b0cdbd9aac696090b833cc6c9c1750d653f82a2d1f1e4c3e16db1950d749c
Transactions (1)
Coinbase491b0cdbd9aac6…e16db1950d749c
1 in β†’ 1 out7.4000 XPM110 B
AZooZriE…NHNy9M5b
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.426 Γ— 10⁹³(94-digit number)
24265852354062603719…56000202611629054770
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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.

1
origin βˆ’ 1
2.426 Γ— 10⁹³(94-digit number)
24265852354062603719…56000202611629054769
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.853 Γ— 10⁹³(94-digit number)
48531704708125207438…12000405223258109539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.706 Γ— 10⁹³(94-digit number)
97063409416250414877…24000810446516219079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.941 Γ— 10⁹⁴(95-digit number)
19412681883250082975…48001620893032438159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.882 Γ— 10⁹⁴(95-digit number)
38825363766500165951…96003241786064876319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.765 Γ— 10⁹⁴(95-digit number)
77650727533000331902…92006483572129752639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.553 Γ— 10⁹⁡(96-digit number)
15530145506600066380…84012967144259505279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.106 Γ— 10⁹⁡(96-digit number)
31060291013200132760…68025934288519010559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.212 Γ— 10⁹⁡(96-digit number)
62120582026400265521…36051868577038021119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.242 Γ— 10⁹⁢(97-digit number)
12424116405280053104…72103737154076042239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.484 Γ— 10⁹⁢(97-digit number)
24848232810560106208…44207474308152084479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2716659

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 6fba4510cc8ef4888207bb16e1c78f0cc71b5bb572e0c3ff182779c15fe865bf

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 β†’ Debug Window β†’ 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 #2,716,659 on Chainz β†—
Circulating Supply:57,993,866 XPMΒ·at block #6,843,686 Β· updates every 60s
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