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Block #79,809

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2013, 6:12:35 PM Β· Difficulty 9.2430 Β· 6,714,599 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6fdedfb82d36afb722e93f609b89e7138c7231f49b33431c78e574c903e3bf35
View on Chainz β†—

Height

#79,809

Difficulty

9.243050

Transactions

1

Size

195 B

Version

2

Bits

093e3881

Nonce

384

Timestamp

7/23/2013, 6:12:35 PM

Confirmations

6,714,599

Merkle Root

a5b01cec1c4c68cbe9b69ec301aec5a08ad691e51913e1125d48d163ca15347f
Transactions (1)
Coinbasea5b01cec1c4c68…48d163ca15347f
1 in β†’ 1 out11.6900 XPM110 B
ALqzbGAB…FEUzNCWa
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.

3.545 Γ— 10⁸³(84-digit number)
35451393634474771053…48242332072063240500
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
3.545 Γ— 10⁸³(84-digit number)
35451393634474771053…48242332072063240499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.090 Γ— 10⁸³(84-digit number)
70902787268949542106…96484664144126480999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.418 Γ— 10⁸⁴(85-digit number)
14180557453789908421…92969328288252961999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.836 Γ— 10⁸⁴(85-digit number)
28361114907579816842…85938656576505923999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.672 Γ— 10⁸⁴(85-digit number)
56722229815159633685…71877313153011847999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.134 Γ— 10⁸⁡(86-digit number)
11344445963031926737…43754626306023695999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.268 Γ— 10⁸⁡(86-digit number)
22688891926063853474…87509252612047391999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.537 Γ— 10⁸⁡(86-digit number)
45377783852127706948…75018505224094783999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.075 Γ— 10⁸⁡(86-digit number)
90755567704255413896…50037010448189567999
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 79809

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 6fdedfb82d36afb722e93f609b89e7138c7231f49b33431c78e574c903e3bf35

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 #79,809 on Chainz β†—
Circulating Supply:57,599,296 XPMΒ·at block #6,794,407 Β· updates every 60s
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