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Block #59,352

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/18/2013, 1:37:21 AM Β· Difficulty 8.9646 Β· 6,739,527 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ebfe0e038fc8c7ca257db42f78ed4098432f251e9b26b92a6eb60be52c899388
View on Chainz β†—

Height

#59,352

Difficulty

8.964554

Transactions

1

Size

199 B

Version

2

Bits

08f6ecfb

Nonce

749

Timestamp

7/18/2013, 1:37:21 AM

Confirmations

6,739,527

Merkle Root

23d04d5f6b732d17a3be96966235f1ae38e00aa518b0e933ea2981547ace40d5
Transactions (1)
Coinbase23d04d5f6b732d…2981547ace40d5
1 in β†’ 1 out12.4300 XPM110 B
AQpp1YkG…KjtErRjr
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.

2.256 Γ— 10⁹²(93-digit number)
22561257831127310899…18757939016788488000
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
2.256 Γ— 10⁹²(93-digit number)
22561257831127310899…18757939016788487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.512 Γ— 10⁹²(93-digit number)
45122515662254621799…37515878033576975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.024 Γ— 10⁹²(93-digit number)
90245031324509243598…75031756067153951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.804 Γ— 10⁹³(94-digit number)
18049006264901848719…50063512134307903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.609 Γ— 10⁹³(94-digit number)
36098012529803697439…00127024268615807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.219 Γ— 10⁹³(94-digit number)
72196025059607394879…00254048537231615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.443 Γ— 10⁹⁴(95-digit number)
14439205011921478975…00508097074463231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.887 Γ— 10⁹⁴(95-digit number)
28878410023842957951…01016194148926463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.775 Γ— 10⁹⁴(95-digit number)
57756820047685915903…02032388297852927999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 59352

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 ebfe0e038fc8c7ca257db42f78ed4098432f251e9b26b92a6eb60be52c899388

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 #59,352 on Chainz β†—
Circulating Supply:57,635,069 XPMΒ·at block #6,798,878 Β· updates every 60s
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