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Block #752,281

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/4/2014, 4:00:20 PM Β· Difficulty 10.9733 Β· 6,073,242 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ddc6bdbe298bea8fe97e85c273d00ec03ce04e26b0d05d7876933b76be93f770
View on Chainz β†—

Height

#752,281

Difficulty

10.973275

Transactions

1

Size

198 B

Version

2

Bits

0af9288a

Nonce

691,059,587

Timestamp

10/4/2014, 4:00:20 PM

Confirmations

6,073,242

Merkle Root

554f00b19f1dfaa9679642ea1b4b8eb97218884322c39d7051d1ca5bab4072be
Transactions (1)
Coinbase554f00b19f1dfa…d1ca5bab4072be
1 in β†’ 1 out8.2900 XPM109 B
AHrjaKNJ…snz3hWts
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.

1.462 Γ— 10⁹²(93-digit number)
14628368908226710695…46863349000198771760
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
1.462 Γ— 10⁹²(93-digit number)
14628368908226710695…46863349000198771759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.925 Γ— 10⁹²(93-digit number)
29256737816453421391…93726698000397543519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.851 Γ— 10⁹²(93-digit number)
58513475632906842783…87453396000795087039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.170 Γ— 10⁹³(94-digit number)
11702695126581368556…74906792001590174079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.340 Γ— 10⁹³(94-digit number)
23405390253162737113…49813584003180348159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.681 Γ— 10⁹³(94-digit number)
46810780506325474226…99627168006360696319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.362 Γ— 10⁹³(94-digit number)
93621561012650948453…99254336012721392639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.872 Γ— 10⁹⁴(95-digit number)
18724312202530189690…98508672025442785279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.744 Γ— 10⁹⁴(95-digit number)
37448624405060379381…97017344050885570559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.489 Γ— 10⁹⁴(95-digit number)
74897248810120758763…94034688101771141119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.497 Γ— 10⁹⁡(96-digit number)
14979449762024151752…88069376203542282239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 752281

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 ddc6bdbe298bea8fe97e85c273d00ec03ce04e26b0d05d7876933b76be93f770

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 #752,281 on Chainz β†—
Circulating Supply:57,848,280 XPMΒ·at block #6,825,522 Β· updates every 60s
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