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Home/Chain Registry/Block #2,682,008

Block #2,682,008

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/28/2018, 8:01:13 PM Β· Difficulty 11.6905 Β· 4,160,396 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ccb9e94ce0e23dd0020ad56653b5ee84e387651c53b395358e6ed0025ee7be3
View on Chainz β†—

Difficulty

11.690523

Transactions

1

Size

200 B

Version

2

Bits

0bb0c622

Nonce

3,631,375

Timestamp

5/28/2018, 8:01:13 PM

Confirmations

4,160,396

Merkle Root

76b4812fc24e4a799da1c484d089375f41a016a1b942c105b1635f7e3cd03b51
Transactions (1)
Coinbase76b4812fc24e4a…635f7e3cd03b51
1 in β†’ 1 out7.3000 XPM110 B
AaHvaCP1…gG8hrr6Q
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.

2.644 Γ— 10⁹⁴(95-digit number)
26440397187435362652…97806576694145285600
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
2.644 Γ— 10⁹⁴(95-digit number)
26440397187435362652…97806576694145285601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.288 Γ— 10⁹⁴(95-digit number)
52880794374870725305…95613153388290571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.057 Γ— 10⁹⁡(96-digit number)
10576158874974145061…91226306776581142401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.115 Γ— 10⁹⁡(96-digit number)
21152317749948290122…82452613553162284801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.230 Γ— 10⁹⁡(96-digit number)
42304635499896580244…64905227106324569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.460 Γ— 10⁹⁡(96-digit number)
84609270999793160488…29810454212649139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.692 Γ— 10⁹⁢(97-digit number)
16921854199958632097…59620908425298278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.384 Γ— 10⁹⁢(97-digit number)
33843708399917264195…19241816850596556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.768 Γ— 10⁹⁢(97-digit number)
67687416799834528390…38483633701193113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.353 Γ— 10⁹⁷(98-digit number)
13537483359966905678…76967267402386227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.707 Γ— 10⁹⁷(98-digit number)
27074966719933811356…53934534804772454401
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2682008

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 2ccb9e94ce0e23dd0020ad56653b5ee84e387651c53b395358e6ed0025ee7be3

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 #2,682,008 on Chainz β†—
Circulating Supply:57,983,644 XPMΒ·at block #6,842,403 Β· updates every 60s
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