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Block #152,540

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 9:46:09 AM Β· Difficulty 9.8625 Β· 6,663,423 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d890a763de36c758074c20d87d7501e8a07ec97657140f4148266111d8e489f
View on Chainz β†—

Height

#152,540

Difficulty

9.862457

Transactions

1

Size

199 B

Version

2

Bits

09dcc9fe

Nonce

30,332

Timestamp

9/6/2013, 9:46:09 AM

Confirmations

6,663,423

Merkle Root

710b8a6c1f7e89c02a055b8aaa92925f23e6c4156664473adaa6f9f51593db89
Transactions (1)
Coinbase710b8a6c1f7e89…a6f9f51593db89
1 in β†’ 1 out10.2700 XPM109 B
ASiN1vnG…nPBYx4TC
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.

3.619 Γ— 10⁹⁡(96-digit number)
36191505311096956862…10978389063892731680
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
3.619 Γ— 10⁹⁡(96-digit number)
36191505311096956862…10978389063892731679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.238 Γ— 10⁹⁡(96-digit number)
72383010622193913724…21956778127785463359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.447 Γ— 10⁹⁢(97-digit number)
14476602124438782744…43913556255570926719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.895 Γ— 10⁹⁢(97-digit number)
28953204248877565489…87827112511141853439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.790 Γ— 10⁹⁢(97-digit number)
57906408497755130979…75654225022283706879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.158 Γ— 10⁹⁷(98-digit number)
11581281699551026195…51308450044567413759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.316 Γ— 10⁹⁷(98-digit number)
23162563399102052391…02616900089134827519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.632 Γ— 10⁹⁷(98-digit number)
46325126798204104783…05233800178269655039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.265 Γ— 10⁹⁷(98-digit number)
92650253596408209566…10467600356539310079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.853 Γ— 10⁹⁸(99-digit number)
18530050719281641913…20935200713078620159
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 152540

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 4d890a763de36c758074c20d87d7501e8a07ec97657140f4148266111d8e489f

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 #152,540 on Chainz β†—
Circulating Supply:57,771,819 XPMΒ·at block #6,815,962 Β· updates every 60s
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