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Home/Chain Registry/Block #2,652,578

Block #2,652,578

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/7/2018, 5:19:34 PM Β· Difficulty 11.7440 Β· 4,191,962 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6a5294fa536dd2e195e9785d8ea481bd70b3982b8424c2a3d3fd618b3841d9fd
View on Chainz β†—

Difficulty

11.743969

Transactions

1

Size

201 B

Version

2

Bits

0bbe74c2

Nonce

1,176,357,081

Timestamp

5/7/2018, 5:19:34 PM

Confirmations

4,191,962

Merkle Root

933be90f6adecbe61d1fb9b4b8b75cfb3cc431efb27bc9fa16f4b8c5aeaab620
Transactions (1)
Coinbase933be90f6adecb…f4b8c5aeaab620
1 in β†’ 1 out7.2400 XPM110 B
AVqW7AnD…JCnKnjoT
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.

7.316 Γ— 10⁹⁡(96-digit number)
73160235149709967647…79401375704439511040
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
7.316 Γ— 10⁹⁡(96-digit number)
73160235149709967647…79401375704439511039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.463 Γ— 10⁹⁢(97-digit number)
14632047029941993529…58802751408879022079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.926 Γ— 10⁹⁢(97-digit number)
29264094059883987058…17605502817758044159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.852 Γ— 10⁹⁢(97-digit number)
58528188119767974117…35211005635516088319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.170 Γ— 10⁹⁷(98-digit number)
11705637623953594823…70422011271032176639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.341 Γ— 10⁹⁷(98-digit number)
23411275247907189647…40844022542064353279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.682 Γ— 10⁹⁷(98-digit number)
46822550495814379294…81688045084128706559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.364 Γ— 10⁹⁷(98-digit number)
93645100991628758588…63376090168257413119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.872 Γ— 10⁹⁸(99-digit number)
18729020198325751717…26752180336514826239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.745 Γ— 10⁹⁸(99-digit number)
37458040396651503435…53504360673029652479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.491 Γ— 10⁹⁸(99-digit number)
74916080793303006870…07008721346059304959
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 2652578

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 6a5294fa536dd2e195e9785d8ea481bd70b3982b8424c2a3d3fd618b3841d9fd

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 #2,652,578 on Chainz β†—
Circulating Supply:58,000,723 XPMΒ·at block #6,844,539 Β· updates every 60s
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