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Block #96,023

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/3/2013, 11:53:37 PM Β· Difficulty 9.2517 Β· 6,730,237 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6529955c74f29e718751e7c60e5071f67c1dcf5699d6fcd276aa0690887460b7
View on Chainz β†—

Height

#96,023

Difficulty

9.251732

Transactions

1

Size

214 B

Version

2

Bits

09407188

Nonce

1,484

Timestamp

8/3/2013, 11:53:37 PM

Confirmations

6,730,237

Merkle Root

fc558dff85730a5292347ee13fcb2c62b2edfe804943e00daf77b31443069dbc
Transactions (1)
Coinbasefc558dff85730a…77b31443069dbc
1 in β†’ 1 out11.6700 XPM112 B
AT5A2KL6…CT16n6i2
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.

9.865 Γ— 10ΒΉΒ²Β²(123-digit number)
98657546533066949669…01271469930861111160
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
9.865 Γ— 10ΒΉΒ²Β²(123-digit number)
98657546533066949669…01271469930861111159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.973 Γ— 10ΒΉΒ²Β³(124-digit number)
19731509306613389933…02542939861722222319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.946 Γ— 10ΒΉΒ²Β³(124-digit number)
39463018613226779867…05085879723444444639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.892 Γ— 10ΒΉΒ²Β³(124-digit number)
78926037226453559735…10171759446888889279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.578 Γ— 10¹²⁴(125-digit number)
15785207445290711947…20343518893777778559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.157 Γ— 10¹²⁴(125-digit number)
31570414890581423894…40687037787555557119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.314 Γ— 10¹²⁴(125-digit number)
63140829781162847788…81374075575111114239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.262 Γ— 10¹²⁡(126-digit number)
12628165956232569557…62748151150222228479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.525 Γ— 10¹²⁡(126-digit number)
25256331912465139115…25496302300444456959
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 96023

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 6529955c74f29e718751e7c60e5071f67c1dcf5699d6fcd276aa0690887460b7

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 #96,023 on Chainz β†—
Circulating Supply:57,854,214 XPMΒ·at block #6,826,259 Β· updates every 60s
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