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Block #54,249

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 7:27:36 PM Β· Difficulty 8.9317 Β· 6,759,764 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a5c48c1398f1a61ad5a99e2f58060c6f20505bb50d1ea2b2b9a87c69a8e51b2f
View on Chainz β†—

Height

#54,249

Difficulty

8.931650

Transactions

1

Size

197 B

Version

2

Bits

08ee809f

Nonce

25

Timestamp

7/16/2013, 7:27:36 PM

Confirmations

6,759,764

Merkle Root

9d586d74bc0999abfc0cc7174fe3b6693d5819b0d8cfbd6ef0eecbab0315399a
Transactions (1)
Coinbase9d586d74bc0999…eecbab0315399a
1 in β†’ 1 out12.5200 XPM110 B
AJbz55M2…moHxsz79
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.

7.288 Γ— 10⁸⁢(87-digit number)
72889556189278468528…99261438328329312540
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
7.288 Γ— 10⁸⁢(87-digit number)
72889556189278468528…99261438328329312539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.457 Γ— 10⁸⁷(88-digit number)
14577911237855693705…98522876656658625079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.915 Γ— 10⁸⁷(88-digit number)
29155822475711387411…97045753313317250159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.831 Γ— 10⁸⁷(88-digit number)
58311644951422774822…94091506626634500319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.166 Γ— 10⁸⁸(89-digit number)
11662328990284554964…88183013253269000639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.332 Γ— 10⁸⁸(89-digit number)
23324657980569109928…76366026506538001279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.664 Γ— 10⁸⁸(89-digit number)
46649315961138219857…52732053013076002559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.329 Γ— 10⁸⁸(89-digit number)
93298631922276439715…05464106026152005119
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 54249

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 a5c48c1398f1a61ad5a99e2f58060c6f20505bb50d1ea2b2b9a87c69a8e51b2f

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 #54,249 on Chainz β†—
Circulating Supply:57,756,187 XPMΒ·at block #6,814,012 Β· updates every 60s
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