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Block #71,423

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 6:36:43 PM Β· Difficulty 8.9932 Β· 6,742,691 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
596e32340eb46ddc6d949ea0dcc76ad89c81d33d427159c03e9b143c3609731d
View on Chainz β†—

Height

#71,423

Difficulty

8.993175

Transactions

1

Size

200 B

Version

2

Bits

08fe40b5

Nonce

209

Timestamp

7/20/2013, 6:36:43 PM

Confirmations

6,742,691

Merkle Root

7d23654afd275fabc1cfde9fe02aa535201df301f15de7a0b5936aa9e2a31333
Transactions (1)
Coinbase7d23654afd275f…936aa9e2a31333
1 in β†’ 1 out12.3500 XPM110 B
AXSfSc5i…4hVSWmxb
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.

2.659 Γ— 10⁹⁴(95-digit number)
26592337114158200324…90816942879754609250
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
2.659 Γ— 10⁹⁴(95-digit number)
26592337114158200324…90816942879754609249
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.318 Γ— 10⁹⁴(95-digit number)
53184674228316400649…81633885759509218499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.063 Γ— 10⁹⁡(96-digit number)
10636934845663280129…63267771519018436999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.127 Γ— 10⁹⁡(96-digit number)
21273869691326560259…26535543038036873999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.254 Γ— 10⁹⁡(96-digit number)
42547739382653120519…53071086076073747999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.509 Γ— 10⁹⁡(96-digit number)
85095478765306241039…06142172152147495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.701 Γ— 10⁹⁢(97-digit number)
17019095753061248207…12284344304294991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.403 Γ— 10⁹⁢(97-digit number)
34038191506122496415…24568688608589983999
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 71423

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 596e32340eb46ddc6d949ea0dcc76ad89c81d33d427159c03e9b143c3609731d

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 #71,423 on Chainz β†—
Circulating Supply:57,756,994 XPMΒ·at block #6,814,113 Β· updates every 60s
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