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Home/Chain Registry/Block #2,648,890

Block #2,648,890

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 8:30:14 PM Β· Difficulty 11.7656 Β· 4,184,684 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a0cffe478dae0012266d6baa9c6f5866e186da2f14b4907d25e7c56e5bfc844c
View on Chainz β†—

Difficulty

11.765563

Transactions

2

Size

505 B

Version

2

Bits

0bc3fbf5

Nonce

1,105,122,626

Timestamp

5/4/2018, 8:30:14 PM

Confirmations

4,184,684

Merkle Root

aa8b2149f3c7f3ae234c44c4a1e661e6299002ca58ba1c692f65747fb8d36d7c
Transactions (2)
Coinbasecd7860e9fda331…acbfd13a4f3b65
1 in β†’ 1 out7.2200 XPM110 B
AXqhdW3M…TitDW5sh
18df81ba709174…bfd9da6c61e27d
2 in β†’ 2 out14.5000 XPM306 B
AXkG7ZJ5…1HuHWQo8Aav54QHW…JUf589Le
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.

1.141 Γ— 10⁹²(93-digit number)
11411765356247097294…07307375329453571760
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
1.141 Γ— 10⁹²(93-digit number)
11411765356247097294…07307375329453571759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.282 Γ— 10⁹²(93-digit number)
22823530712494194588…14614750658907143519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.564 Γ— 10⁹²(93-digit number)
45647061424988389177…29229501317814287039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.129 Γ— 10⁹²(93-digit number)
91294122849976778355…58459002635628574079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.825 Γ— 10⁹³(94-digit number)
18258824569995355671…16918005271257148159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.651 Γ— 10⁹³(94-digit number)
36517649139990711342…33836010542514296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.303 Γ— 10⁹³(94-digit number)
73035298279981422684…67672021085028592639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.460 Γ— 10⁹⁴(95-digit number)
14607059655996284536…35344042170057185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.921 Γ— 10⁹⁴(95-digit number)
29214119311992569073…70688084340114370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.842 Γ— 10⁹⁴(95-digit number)
58428238623985138147…41376168680228741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁡(96-digit number)
11685647724797027629…82752337360457482239
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 2648890

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 a0cffe478dae0012266d6baa9c6f5866e186da2f14b4907d25e7c56e5bfc844c

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 #2,648,890 on Chainz β†—
Circulating Supply:57,912,796 XPMΒ·at block #6,833,573 Β· updates every 60s
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