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Block #32,457

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 2:48:20 AM Β· Difficulty 7.9904 Β· 6,793,756 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a68eec34a389b4be337ff6c957cf65da8d3c5f19b39ab33e192413946ed0d1f7
View on Chainz β†—

Height

#32,457

Difficulty

7.990410

Transactions

1

Size

200 B

Version

2

Bits

07fd8b86

Nonce

936

Timestamp

7/14/2013, 2:48:20 AM

Confirmations

6,793,756

Merkle Root

29690a4857d499ebf9c311826141cf8c81caf99b5d128de46edb3bc432e39044
Transactions (1)
Coinbase29690a4857d499…db3bc432e39044
1 in β†’ 1 out15.6400 XPM109 B
AQmVNoHY…HAoCFejv
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.

3.086 Γ— 10⁹⁷(98-digit number)
30869381714987983049…02577954422551363080
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
3.086 Γ— 10⁹⁷(98-digit number)
30869381714987983049…02577954422551363079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.173 Γ— 10⁹⁷(98-digit number)
61738763429975966099…05155908845102726159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.234 Γ— 10⁹⁸(99-digit number)
12347752685995193219…10311817690205452319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.469 Γ— 10⁹⁸(99-digit number)
24695505371990386439…20623635380410904639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.939 Γ— 10⁹⁸(99-digit number)
49391010743980772879…41247270760821809279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.878 Γ— 10⁹⁸(99-digit number)
98782021487961545759…82494541521643618559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.975 Γ— 10⁹⁹(100-digit number)
19756404297592309151…64989083043287237119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.951 Γ— 10⁹⁹(100-digit number)
39512808595184618303…29978166086574474239
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 32457

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 a68eec34a389b4be337ff6c957cf65da8d3c5f19b39ab33e192413946ed0d1f7

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 #32,457 on Chainz β†—
Circulating Supply:57,853,836 XPMΒ·at block #6,826,212 Β· updates every 60s
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