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Block #69,309

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 8:08:54 AM Β· Difficulty 8.9908 Β· 6,738,011 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ed44aa90f91e33c95a76a9b1121e923a43c06ee56f53ebcaec193b61d4b06e16
View on Chainz β†—

Height

#69,309

Difficulty

8.990761

Transactions

1

Size

199 B

Version

2

Bits

08fda28a

Nonce

616

Timestamp

7/20/2013, 8:08:54 AM

Confirmations

6,738,011

Merkle Root

82811cf0a63b7ca819ef0225c26c54dcd48f1fd7ac8978871708d34a1a7ec99c
Transactions (1)
Coinbase82811cf0a63b7c…08d34a1a7ec99c
1 in β†’ 1 out12.3500 XPM110 B
APxUMipn…2zpbPwcA
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.

1.432 Γ— 10⁹¹(92-digit number)
14322565160832864843…34291235377652808800
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
1.432 Γ— 10⁹¹(92-digit number)
14322565160832864843…34291235377652808799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.864 Γ— 10⁹¹(92-digit number)
28645130321665729687…68582470755305617599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.729 Γ— 10⁹¹(92-digit number)
57290260643331459374…37164941510611235199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.145 Γ— 10⁹²(93-digit number)
11458052128666291874…74329883021222470399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.291 Γ— 10⁹²(93-digit number)
22916104257332583749…48659766042444940799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.583 Γ— 10⁹²(93-digit number)
45832208514665167499…97319532084889881599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.166 Γ— 10⁹²(93-digit number)
91664417029330334998…94639064169779763199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.833 Γ— 10⁹³(94-digit number)
18332883405866066999…89278128339559526399
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 69309

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 ed44aa90f91e33c95a76a9b1121e923a43c06ee56f53ebcaec193b61d4b06e16

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 #69,309 on Chainz β†—
Circulating Supply:57,702,576 XPMΒ·at block #6,807,319 Β· updates every 60s
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