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Home/Chain Registry/Block #2,651,446

Block #2,651,446

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/6/2018, 8:08:52 PM Β· Difficulty 11.7508 Β· 4,189,634 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1dd258b35d11effbb80036939ea0a92f6bca5d9e1694764476ae93dc5fafe7a2
View on Chainz β†—

Difficulty

11.750849

Transactions

1

Size

200 B

Version

2

Bits

0bc0379f

Nonce

426,039,903

Timestamp

5/6/2018, 8:08:52 PM

Confirmations

4,189,634

Merkle Root

f325a46aa1c7b7b093d19bcd2dc3626358fe553cc157bb82c5193289379b8045
Transactions (1)
Coinbasef325a46aa1c7b7…193289379b8045
1 in β†’ 1 out7.2300 XPM110 B
AMHZnDjq…ELHF8EH7
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.

5.947 Γ— 10⁹⁴(95-digit number)
59471074796636111363…44911556238320273760
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
5.947 Γ— 10⁹⁴(95-digit number)
59471074796636111363…44911556238320273759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.189 Γ— 10⁹⁡(96-digit number)
11894214959327222272…89823112476640547519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.378 Γ— 10⁹⁡(96-digit number)
23788429918654444545…79646224953281095039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.757 Γ— 10⁹⁡(96-digit number)
47576859837308889090…59292449906562190079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.515 Γ— 10⁹⁡(96-digit number)
95153719674617778181…18584899813124380159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁢(97-digit number)
19030743934923555636…37169799626248760319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.806 Γ— 10⁹⁢(97-digit number)
38061487869847111272…74339599252497520639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.612 Γ— 10⁹⁢(97-digit number)
76122975739694222545…48679198504995041279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.522 Γ— 10⁹⁷(98-digit number)
15224595147938844509…97358397009990082559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.044 Γ— 10⁹⁷(98-digit number)
30449190295877689018…94716794019980165119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.089 Γ— 10⁹⁷(98-digit number)
60898380591755378036…89433588039960330239
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 2651446

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 1dd258b35d11effbb80036939ea0a92f6bca5d9e1694764476ae93dc5fafe7a2

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 #2,651,446 on Chainz β†—
Circulating Supply:57,973,002 XPMΒ·at block #6,841,079 Β· updates every 60s
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