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Block #79,898

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2013, 7:50:53 PM Β· Difficulty 9.2416 Β· 6,747,022 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
28c774dfa390c633d8d4fbf051cad190caece3a3c34b0a6b2c81a593ef6decd1
View on Chainz β†—

Height

#79,898

Difficulty

9.241569

Transactions

1

Size

200 B

Version

2

Bits

093dd777

Nonce

530

Timestamp

7/23/2013, 7:50:53 PM

Confirmations

6,747,022

Merkle Root

eb9fdc0d277509e619b6423d550f5afb8a83fb7e8d0233761f915bcf4c4b094f
Transactions (1)
Coinbaseeb9fdc0d277509…915bcf4c4b094f
1 in β†’ 1 out11.6900 XPM110 B
AYLS7Nvq…43exfVqt
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.

6.428 Γ— 10⁹⁴(95-digit number)
64288384137726545737…65215413808370700800
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
6.428 Γ— 10⁹⁴(95-digit number)
64288384137726545737…65215413808370700799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.285 Γ— 10⁹⁡(96-digit number)
12857676827545309147…30430827616741401599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.571 Γ— 10⁹⁡(96-digit number)
25715353655090618294…60861655233482803199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.143 Γ— 10⁹⁡(96-digit number)
51430707310181236589…21723310466965606399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁢(97-digit number)
10286141462036247317…43446620933931212799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.057 Γ— 10⁹⁢(97-digit number)
20572282924072494635…86893241867862425599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.114 Γ— 10⁹⁢(97-digit number)
41144565848144989271…73786483735724851199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.228 Γ— 10⁹⁢(97-digit number)
82289131696289978543…47572967471449702399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.645 Γ— 10⁹⁷(98-digit number)
16457826339257995708…95145934942899404799
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 79898

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 28c774dfa390c633d8d4fbf051cad190caece3a3c34b0a6b2c81a593ef6decd1

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 #79,898 on Chainz β†—
Circulating Supply:57,859,530 XPMΒ·at block #6,826,919 Β· updates every 60s
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