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Block #51,998

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 8:19:59 AM Β· Difficulty 8.9063 Β· 6,755,445 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0939c08dc83dc81b3f6bb9a2aeb688ddfcd9157f4fb6d08cc3bdbc65e7065e1
View on Chainz β†—

Height

#51,998

Difficulty

8.906337

Transactions

1

Size

203 B

Version

2

Bits

08e805b3

Nonce

183

Timestamp

7/16/2013, 8:19:59 AM

Confirmations

6,755,445

Merkle Root

2b51e768cbd62b9632e43abf00b1f0eb09fab553b2bbcd462f2fbb163af41ae1
Transactions (1)
Coinbase2b51e768cbd62b…2fbb163af41ae1
1 in β†’ 1 out12.5900 XPM109 B
AX85bWR1…X2GwLbPj
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.

2.483 Γ— 10¹⁰⁡(106-digit number)
24836303674759178436…85869583808289578000
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
2.483 Γ— 10¹⁰⁡(106-digit number)
24836303674759178436…85869583808289577999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.967 Γ— 10¹⁰⁡(106-digit number)
49672607349518356872…71739167616579155999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.934 Γ— 10¹⁰⁡(106-digit number)
99345214699036713744…43478335233158311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.986 Γ— 10¹⁰⁢(107-digit number)
19869042939807342748…86956670466316623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.973 Γ— 10¹⁰⁢(107-digit number)
39738085879614685497…73913340932633247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.947 Γ— 10¹⁰⁢(107-digit number)
79476171759229370995…47826681865266495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.589 Γ— 10¹⁰⁷(108-digit number)
15895234351845874199…95653363730532991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.179 Γ— 10¹⁰⁷(108-digit number)
31790468703691748398…91306727461065983999
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 51998

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 e0939c08dc83dc81b3f6bb9a2aeb688ddfcd9157f4fb6d08cc3bdbc65e7065e1

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 #51,998 on Chainz β†—
Circulating Supply:57,703,565 XPMΒ·at block #6,807,442 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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