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Block #52,485

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 10:33:39 AM Β· Difficulty 8.9127 Β· 6,760,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51262891828fd41794e23930ed6ae42ddd658e599e6f4fe1dd8e097f4c047f96
View on Chainz β†—

Height

#52,485

Difficulty

8.912704

Transactions

1

Size

200 B

Version

2

Bits

08e9a6f8

Nonce

165

Timestamp

7/16/2013, 10:33:39 AM

Confirmations

6,760,481

Merkle Root

73c61bb9f688ed0f118e11c8e293ff1c144e73a34f7e20af87e0d2e6c48a3483
Transactions (1)
Coinbase73c61bb9f688ed…e0d2e6c48a3483
1 in β†’ 1 out12.5700 XPM110 B
ATU8vBma…8ASBo1Y8
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.

1.227 Γ— 10⁹⁴(95-digit number)
12276234307930114260…47339701154852921500
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
1.227 Γ— 10⁹⁴(95-digit number)
12276234307930114260…47339701154852921499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.455 Γ— 10⁹⁴(95-digit number)
24552468615860228520…94679402309705842999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.910 Γ— 10⁹⁴(95-digit number)
49104937231720457041…89358804619411685999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.820 Γ— 10⁹⁴(95-digit number)
98209874463440914083…78717609238823371999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.964 Γ— 10⁹⁡(96-digit number)
19641974892688182816…57435218477646743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.928 Γ— 10⁹⁡(96-digit number)
39283949785376365633…14870436955293487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.856 Γ— 10⁹⁡(96-digit number)
78567899570752731267…29740873910586975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.571 Γ— 10⁹⁢(97-digit number)
15713579914150546253…59481747821173951999
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 52485

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 51262891828fd41794e23930ed6ae42ddd658e599e6f4fe1dd8e097f4c047f96

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 #52,485 on Chainz β†—
Circulating Supply:57,747,771 XPMΒ·at block #6,812,965 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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