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Block #2,641,485

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2018, 9:06:36 AM Β· Difficulty 11.6217 Β· 4,190,064 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f5ea11f77d33526ef82ce48d1edf281cbe353e7bdeccd904f8eee5757a227365
View on Chainz β†—

Difficulty

11.621718

Transactions

1

Size

199 B

Version

2

Bits

0b9f28ed

Nonce

194,248,772

Timestamp

5/1/2018, 9:06:36 AM

Confirmations

4,190,064

Merkle Root

b5517d3c34f128489bdf49cd13a5ba54daf5ee73342e4cc878e967bbc736c758
Transactions (1)
Coinbaseb5517d3c34f128…e967bbc736c758
1 in β†’ 1 out7.3900 XPM110 B
AJW6MYh3…3fTsoBrT
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.

1.115 Γ— 10⁹²(93-digit number)
11152526891323902771…66346980873254693180
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
1.115 Γ— 10⁹²(93-digit number)
11152526891323902771…66346980873254693179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.230 Γ— 10⁹²(93-digit number)
22305053782647805543…32693961746509386359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.461 Γ— 10⁹²(93-digit number)
44610107565295611086…65387923493018772719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.922 Γ— 10⁹²(93-digit number)
89220215130591222173…30775846986037545439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.784 Γ— 10⁹³(94-digit number)
17844043026118244434…61551693972075090879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.568 Γ— 10⁹³(94-digit number)
35688086052236488869…23103387944150181759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.137 Γ— 10⁹³(94-digit number)
71376172104472977738…46206775888300363519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.427 Γ— 10⁹⁴(95-digit number)
14275234420894595547…92413551776600727039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.855 Γ— 10⁹⁴(95-digit number)
28550468841789191095…84827103553201454079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.710 Γ— 10⁹⁴(95-digit number)
57100937683578382191…69654207106402908159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.142 Γ— 10⁹⁡(96-digit number)
11420187536715676438…39308414212805816319
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 2641485

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 f5ea11f77d33526ef82ce48d1edf281cbe353e7bdeccd904f8eee5757a227365

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 #2,641,485 on Chainz β†—
Circulating Supply:57,896,483 XPMΒ·at block #6,831,548 Β· updates every 60s
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