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Block #52,128

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 8:56:40 AM Β· Difficulty 8.9081 Β· 6,774,355 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cbdfe52b448bd517a65c747ec6d108de0a498796ba0175bb487b0c112252c780
View on Chainz β†—

Height

#52,128

Difficulty

8.908063

Transactions

1

Size

198 B

Version

2

Bits

08e876d9

Nonce

30

Timestamp

7/16/2013, 8:56:40 AM

Confirmations

6,774,355

Merkle Root

1e6ba53c01c97d488b71b89ef48f9fcc1e85d00556085012f54cce540b2ebc3d
Transactions (1)
Coinbase1e6ba53c01c97d…4cce540b2ebc3d
1 in β†’ 1 out12.5800 XPM110 B
AcigRCz6…VHpxh7x4
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.

1.628 Γ— 10⁹⁰(91-digit number)
16282411436760891940…56721984450199887360
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
1.628 Γ— 10⁹⁰(91-digit number)
16282411436760891940…56721984450199887359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.256 Γ— 10⁹⁰(91-digit number)
32564822873521783881…13443968900399774719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.512 Γ— 10⁹⁰(91-digit number)
65129645747043567762…26887937800799549439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.302 Γ— 10⁹¹(92-digit number)
13025929149408713552…53775875601599098879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.605 Γ— 10⁹¹(92-digit number)
26051858298817427104…07551751203198197759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.210 Γ— 10⁹¹(92-digit number)
52103716597634854209…15103502406396395519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.042 Γ— 10⁹²(93-digit number)
10420743319526970841…30207004812792791039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.084 Γ— 10⁹²(93-digit number)
20841486639053941683…60414009625585582079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 52128

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 cbdfe52b448bd517a65c747ec6d108de0a498796ba0175bb487b0c112252c780

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 #52,128 on Chainz β†—
Circulating Supply:57,856,003 XPMΒ·at block #6,826,482 Β· updates every 60s
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