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Block #75,085

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 2:33:23 PM Β· Difficulty 8.9959 Β· 6,721,061 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fb6e5a3ada7e9ebfae73cb3bc5ba1aa884b72e544c79cfee5f59aa8f2df9a6b8
View on Chainz β†—

Height

#75,085

Difficulty

8.995902

Transactions

1

Size

200 B

Version

2

Bits

08fef36e

Nonce

230

Timestamp

7/21/2013, 2:33:23 PM

Confirmations

6,721,061

Merkle Root

d6f7cd3276bf8ddc6a4c2c7ce05255fce2402585fff94686d69498c5f4851b51
Transactions (1)
Coinbased6f7cd3276bf8d…9498c5f4851b51
1 in β†’ 1 out12.3400 XPM110 B
AHrAFQUw…YAZsY75F
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.

1.883 Γ— 10⁹⁡(96-digit number)
18839140449054223247…92107858027801189800
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
1.883 Γ— 10⁹⁡(96-digit number)
18839140449054223247…92107858027801189799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.767 Γ— 10⁹⁡(96-digit number)
37678280898108446494…84215716055602379599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.535 Γ— 10⁹⁡(96-digit number)
75356561796216892989…68431432111204759199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.507 Γ— 10⁹⁢(97-digit number)
15071312359243378597…36862864222409518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.014 Γ— 10⁹⁢(97-digit number)
30142624718486757195…73725728444819036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.028 Γ— 10⁹⁢(97-digit number)
60285249436973514391…47451456889638073599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.205 Γ— 10⁹⁷(98-digit number)
12057049887394702878…94902913779276147199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.411 Γ— 10⁹⁷(98-digit number)
24114099774789405756…89805827558552294399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.822 Γ— 10⁹⁷(98-digit number)
48228199549578811513…79611655117104588799
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 75085

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 fb6e5a3ada7e9ebfae73cb3bc5ba1aa884b72e544c79cfee5f59aa8f2df9a6b8

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 #75,085 on Chainz β†—
Circulating Supply:57,613,166 XPMΒ·at block #6,796,145 Β· updates every 60s
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