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Home/Chain Registry/Block #2,639,998

Block #2,639,998

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/30/2018, 8:36:44 PM Β· Difficulty 11.5621 Β· 4,192,686 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
27ecfccf7ff20fcbc47eeef8280cf70af2e4b219b227eefc10b6a6170db98358
View on Chainz β†—

Difficulty

11.562075

Transactions

1

Size

200 B

Version

2

Bits

0b8fe421

Nonce

1,431,940,289

Timestamp

4/30/2018, 8:36:44 PM

Confirmations

4,192,686

Merkle Root

6f71cbdbe3f363ad405071f513e86f31b3831856896cad2e39949b109cad6557
Transactions (1)
Coinbase6f71cbdbe3f363…949b109cad6557
1 in β†’ 1 out7.4700 XPM110 B
AWcmjakq…GEV75GPD
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.

6.717 Γ— 10⁹⁴(95-digit number)
67177447043196420318…53008137623240775680
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
6.717 Γ— 10⁹⁴(95-digit number)
67177447043196420318…53008137623240775679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁡(96-digit number)
13435489408639284063…06016275246481551359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.687 Γ— 10⁹⁡(96-digit number)
26870978817278568127…12032550492963102719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.374 Γ— 10⁹⁡(96-digit number)
53741957634557136255…24065100985926205439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁢(97-digit number)
10748391526911427251…48130201971852410879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁢(97-digit number)
21496783053822854502…96260403943704821759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.299 Γ— 10⁹⁢(97-digit number)
42993566107645709004…92520807887409643519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.598 Γ— 10⁹⁢(97-digit number)
85987132215291418008…85041615774819287039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁷(98-digit number)
17197426443058283601…70083231549638574079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.439 Γ— 10⁹⁷(98-digit number)
34394852886116567203…40166463099277148159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.878 Γ— 10⁹⁷(98-digit number)
68789705772233134406…80332926198554296319
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 2639998

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 27ecfccf7ff20fcbc47eeef8280cf70af2e4b219b227eefc10b6a6170db98358

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 #2,639,998 on Chainz β†—
Circulating Supply:57,905,627 XPMΒ·at block #6,832,683 Β· updates every 60s
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