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Home/Chain Registry/Block #150,952

Block #150,952

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2013, 9:25:15 AM Β· Difficulty 9.8589 Β· 6,663,393 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0b668acea3fb6875327862f4d96eb09bd41fb32ff29a9acbe6bdf35218944e99
View on Chainz β†—

Height

#150,952

Difficulty

9.858889

Transactions

1

Size

198 B

Version

2

Bits

09dbe025

Nonce

46,670

Timestamp

9/5/2013, 9:25:15 AM

Confirmations

6,663,393

Merkle Root

8e19dd45b89d4c2ce5953f56ecde372a40a2e0fb4de491450e61f00436e918bf
Transactions (1)
Coinbase8e19dd45b89d4c…61f00436e918bf
1 in β†’ 1 out10.2700 XPM109 B
AYAJbQxg…XnxvH3gj
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.

1.051 Γ— 10⁹²(93-digit number)
10517218527638231988…68613474586154717420
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.051 Γ— 10⁹²(93-digit number)
10517218527638231988…68613474586154717421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.103 Γ— 10⁹²(93-digit number)
21034437055276463977…37226949172309434841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.206 Γ— 10⁹²(93-digit number)
42068874110552927955…74453898344618869681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.413 Γ— 10⁹²(93-digit number)
84137748221105855911…48907796689237739361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.682 Γ— 10⁹³(94-digit number)
16827549644221171182…97815593378475478721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.365 Γ— 10⁹³(94-digit number)
33655099288442342364…95631186756950957441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.731 Γ— 10⁹³(94-digit number)
67310198576884684729…91262373513901914881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.346 Γ— 10⁹⁴(95-digit number)
13462039715376936945…82524747027803829761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.692 Γ— 10⁹⁴(95-digit number)
26924079430753873891…65049494055607659521
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 150952

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 0b668acea3fb6875327862f4d96eb09bd41fb32ff29a9acbe6bdf35218944e99

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 #150,952 on Chainz β†—
Circulating Supply:57,758,824 XPMΒ·at block #6,814,344 Β· updates every 60s
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