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Block #10,512

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2013, 3:18:27 AM Β· Difficulty 7.6754 Β· 6,796,279 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d8dbae499fca730fdfc21962844e74630148ef8488ac00a75f7c23696f4a04b0
View on Chainz β†—

Height

#10,512

Difficulty

7.675373

Transactions

1

Size

197 B

Version

2

Bits

07ace53d

Nonce

74

Timestamp

7/11/2013, 3:18:27 AM

Confirmations

6,796,279

Merkle Root

e5c193b3e169798794757be9925747b65163d85183bb5f958e06c7fd7357fb6f
Transactions (1)
Coinbasee5c193b3e16979…06c7fd7357fb6f
1 in β†’ 1 out16.9500 XPM108 B
AT5wsBRv…jyjUrFC7
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.

1.626 Γ— 10⁹¹(92-digit number)
16260468076666220536…80583220773044260000
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
1.626 Γ— 10⁹¹(92-digit number)
16260468076666220536…80583220773044259999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.252 Γ— 10⁹¹(92-digit number)
32520936153332441072…61166441546088519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.504 Γ— 10⁹¹(92-digit number)
65041872306664882145…22332883092177039999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.300 Γ— 10⁹²(93-digit number)
13008374461332976429…44665766184354079999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.601 Γ— 10⁹²(93-digit number)
26016748922665952858…89331532368708159999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.203 Γ— 10⁹²(93-digit number)
52033497845331905716…78663064737416319999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.040 Γ— 10⁹³(94-digit number)
10406699569066381143…57326129474832639999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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 7
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 10512

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 d8dbae499fca730fdfc21962844e74630148ef8488ac00a75f7c23696f4a04b0

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 #10,512 on Chainz β†—
Circulating Supply:57,698,433 XPMΒ·at block #6,806,790 Β· updates every 60s
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