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Block #75,113

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 2:46:16 PM Β· Difficulty 8.9959 Β· 6,741,427 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1819a251e88060de9d84c6161141d2a5e18a25b6178f252e8ea886c1b92b9dde
View on Chainz β†—

Height

#75,113

Difficulty

8.995916

Transactions

1

Size

201 B

Version

2

Bits

08fef453

Nonce

597

Timestamp

7/21/2013, 2:46:16 PM

Confirmations

6,741,427

Merkle Root

9094ebaae9f69fba71bde752729f2eb57c02d1b134f59afef55e9bc8a44413b8
Transactions (1)
Coinbase9094ebaae9f69f…5e9bc8a44413b8
1 in β†’ 1 out12.3400 XPM110 B
AHGPtSCN…GESamBFW
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.

2.683 Γ— 10⁹⁢(97-digit number)
26839114540704511258…05753477575585921420
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
2.683 Γ— 10⁹⁢(97-digit number)
26839114540704511258…05753477575585921419
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.367 Γ— 10⁹⁢(97-digit number)
53678229081409022516…11506955151171842839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁷(98-digit number)
10735645816281804503…23013910302343685679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.147 Γ— 10⁹⁷(98-digit number)
21471291632563609006…46027820604687371359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.294 Γ— 10⁹⁷(98-digit number)
42942583265127218013…92055641209374742719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.588 Γ— 10⁹⁷(98-digit number)
85885166530254436026…84111282418749485439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.717 Γ— 10⁹⁸(99-digit number)
17177033306050887205…68222564837498970879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.435 Γ— 10⁹⁸(99-digit number)
34354066612101774410…36445129674997941759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.870 Γ— 10⁹⁸(99-digit number)
68708133224203548821…72890259349995883519
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 75113

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 1819a251e88060de9d84c6161141d2a5e18a25b6178f252e8ea886c1b92b9dde

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 #75,113 on Chainz β†—
Circulating Supply:57,776,448 XPMΒ·at block #6,816,539 Β· updates every 60s
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