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Block #189,556

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/1/2013, 9:36:37 PM Β· Difficulty 9.8733 Β· 6,606,622 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f69d96cda09c47201273ca8bdbab6a7227af50fa7640b8dfaa1d2fd8d48021c2
View on Chainz β†—

Height

#189,556

Difficulty

9.873284

Transactions

1

Size

205 B

Version

2

Bits

09df8f82

Nonce

1,738

Timestamp

10/1/2013, 9:36:37 PM

Confirmations

6,606,622

Merkle Root

43d639b9819eaec25d96db6185670d58c89c6be273423b3bac7d867cc80e1ba3
Transactions (1)
Coinbase43d639b9819eae…7d867cc80e1ba3
1 in β†’ 1 out10.2400 XPM116 B
AcLBm5Z9…S683d7c3
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.

3.428 Γ— 10⁹²(93-digit number)
34289306756300056509…60267865963601318080
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
3.428 Γ— 10⁹²(93-digit number)
34289306756300056509…60267865963601318079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.857 Γ— 10⁹²(93-digit number)
68578613512600113019…20535731927202636159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.371 Γ— 10⁹³(94-digit number)
13715722702520022603…41071463854405272319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.743 Γ— 10⁹³(94-digit number)
27431445405040045207…82142927708810544639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.486 Γ— 10⁹³(94-digit number)
54862890810080090415…64285855417621089279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁴(95-digit number)
10972578162016018083…28571710835242178559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.194 Γ— 10⁹⁴(95-digit number)
21945156324032036166…57143421670484357119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.389 Γ— 10⁹⁴(95-digit number)
43890312648064072332…14286843340968714239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.778 Γ— 10⁹⁴(95-digit number)
87780625296128144664…28573686681937428479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.755 Γ— 10⁹⁡(96-digit number)
17556125059225628932…57147373363874856959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 189556

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 f69d96cda09c47201273ca8bdbab6a7227af50fa7640b8dfaa1d2fd8d48021c2

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 #189,556 on Chainz β†—
Circulating Supply:57,613,423 XPMΒ·at block #6,796,177 Β· updates every 60s
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