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Block #488,421

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/12/2014, 4:52:01 PM Β· Difficulty 10.6549 Β· 6,337,056 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ae5a56be9ce43bd72290d8f63538fe115c926874ac2545af6a4cbedf00a01a21
View on Chainz β†—

Height

#488,421

Difficulty

10.654863

Transactions

2

Size

426 B

Version

2

Bits

0aa7a516

Nonce

15,320,966

Timestamp

4/12/2014, 4:52:01 PM

Confirmations

6,337,056

Merkle Root

41858b4e38de0dbd2ac527453886a8ff9a8a550943c06ee3cf195e1eb9d8c269
Transactions (2)
Coinbase20e39e6bc7ec51…027e976bd51b41
1 in β†’ 1 out8.8000 XPM109 B
AR6bV7NY…SWDJdf9w
4971ce141cfc21…d3c7006eba9e74
1 in β†’ 2 out3.2954 XPM226 B
AYn3Pkxg…qFsdgq7pAaTa1TJW…CS1ZqFKG
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.

1.348 Γ— 10⁹⁷(98-digit number)
13480819068245484706…45557108912964853760
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
1.348 Γ— 10⁹⁷(98-digit number)
13480819068245484706…45557108912964853759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.696 Γ— 10⁹⁷(98-digit number)
26961638136490969412…91114217825929707519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.392 Γ— 10⁹⁷(98-digit number)
53923276272981938824…82228435651859415039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.078 Γ— 10⁹⁸(99-digit number)
10784655254596387764…64456871303718830079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.156 Γ— 10⁹⁸(99-digit number)
21569310509192775529…28913742607437660159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.313 Γ— 10⁹⁸(99-digit number)
43138621018385551059…57827485214875320319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.627 Γ— 10⁹⁸(99-digit number)
86277242036771102119…15654970429750640639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.725 Γ— 10⁹⁹(100-digit number)
17255448407354220423…31309940859501281279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.451 Γ— 10⁹⁹(100-digit number)
34510896814708440847…62619881719002562559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.902 Γ— 10⁹⁹(100-digit number)
69021793629416881695…25239763438005125119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 488421

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 ae5a56be9ce43bd72290d8f63538fe115c926874ac2545af6a4cbedf00a01a21

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 #488,421 on Chainz β†—
Circulating Supply:57,847,910 XPMΒ·at block #6,825,476 Β· updates every 60s
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