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Block #179,072

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/24/2013, 7:53:01 PM Β· Difficulty 9.8639 Β· 6,633,816 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b8cd991b1bb682a1f01d07f80fd680fe0c5f2d1a69be43f39848e08235c4ae36
View on Chainz β†—

Height

#179,072

Difficulty

9.863906

Transactions

1

Size

200 B

Version

2

Bits

09dd28eb

Nonce

86,592

Timestamp

9/24/2013, 7:53:01 PM

Confirmations

6,633,816

Merkle Root

73730ff568f20b6e594bce619d1d6c59a92dbeabb9097eb7b179829d4e66f30b
Transactions (1)
Coinbase73730ff568f20b…79829d4e66f30b
1 in β†’ 1 out10.2600 XPM109 B
AeJkcJGh…QvzeGqxX
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.

3.760 Γ— 10⁹⁷(98-digit number)
37608885916243188824…89721662743392870400
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
3.760 Γ— 10⁹⁷(98-digit number)
37608885916243188824…89721662743392870399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.521 Γ— 10⁹⁷(98-digit number)
75217771832486377649…79443325486785740799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.504 Γ— 10⁹⁸(99-digit number)
15043554366497275529…58886650973571481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.008 Γ— 10⁹⁸(99-digit number)
30087108732994551059…17773301947142963199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.017 Γ— 10⁹⁸(99-digit number)
60174217465989102119…35546603894285926399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.203 Γ— 10⁹⁹(100-digit number)
12034843493197820423…71093207788571852799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.406 Γ— 10⁹⁹(100-digit number)
24069686986395640847…42186415577143705599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.813 Γ— 10⁹⁹(100-digit number)
48139373972791281695…84372831154287411199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.627 Γ— 10⁹⁹(100-digit number)
96278747945582563391…68745662308574822399
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 179072

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 b8cd991b1bb682a1f01d07f80fd680fe0c5f2d1a69be43f39848e08235c4ae36

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 #179,072 on Chainz β†—
Circulating Supply:57,747,134 XPMΒ·at block #6,812,887 Β· updates every 60s
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