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Block #72,811

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2013, 2:23:28 AM Β· Difficulty 8.9944 Β· 6,753,330 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aaf7899d0ec1284786e4e8467f7484a9c7eaabf4a0b54b60309c6a92101508f8
View on Chainz β†—

Height

#72,811

Difficulty

8.994359

Transactions

1

Size

200 B

Version

2

Bits

08fe8e51

Nonce

198

Timestamp

7/21/2013, 2:23:28 AM

Confirmations

6,753,330

Merkle Root

8ebb0d3d1cdd64d38b7b1f87e835adf96dc96eb6f18a7e1bbc8d8e0c5df616ed
Transactions (1)
Coinbase8ebb0d3d1cdd64…8d8e0c5df616ed
1 in β†’ 1 out12.3400 XPM110 B
Acq1hLgp…ahT5ErcF
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.

5.112 Γ— 10⁹⁴(95-digit number)
51121357343434927480…33299437993148273500
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
5.112 Γ— 10⁹⁴(95-digit number)
51121357343434927480…33299437993148273499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.022 Γ— 10⁹⁡(96-digit number)
10224271468686985496…66598875986296546999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.044 Γ— 10⁹⁡(96-digit number)
20448542937373970992…33197751972593093999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.089 Γ— 10⁹⁡(96-digit number)
40897085874747941984…66395503945186187999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.179 Γ— 10⁹⁡(96-digit number)
81794171749495883968…32791007890372375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.635 Γ— 10⁹⁢(97-digit number)
16358834349899176793…65582015780744751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.271 Γ— 10⁹⁢(97-digit number)
32717668699798353587…31164031561489503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.543 Γ— 10⁹⁢(97-digit number)
65435337399596707174…62328063122979007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.308 Γ— 10⁹⁷(98-digit number)
13087067479919341434…24656126245958015999
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 72811

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 aaf7899d0ec1284786e4e8467f7484a9c7eaabf4a0b54b60309c6a92101508f8

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 #72,811 on Chainz β†—
Circulating Supply:57,853,254 XPMΒ·at block #6,826,140 Β· updates every 60s
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