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Home/Chain Registry/Block #135,731

Block #135,731

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2013, 7:25:54 PM Β· Difficulty 9.8121 Β· 6,690,961 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb7c2e8d8970b48a203ae9a750bbdeee2fb4da7cc24b9cef0dea172e61d5c215
View on Chainz β†—

Height

#135,731

Difficulty

9.812132

Transactions

1

Size

197 B

Version

2

Bits

09cfe7da

Nonce

135,402

Timestamp

8/26/2013, 7:25:54 PM

Confirmations

6,690,961

Merkle Root

8aa51708d921799694c847c3ece382fb3d5ad6bc864b0a0cf78bc93dc65a0980
Transactions (1)
Coinbase8aa51708d92179…8bc93dc65a0980
1 in β†’ 1 out10.3700 XPM109 B
AY88KHST…88L8yacq
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.

3.031 Γ— 10⁹⁰(91-digit number)
30319396691150869134…29883674907478698240
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
3.031 Γ— 10⁹⁰(91-digit number)
30319396691150869134…29883674907478698241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.063 Γ— 10⁹⁰(91-digit number)
60638793382301738268…59767349814957396481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.212 Γ— 10⁹¹(92-digit number)
12127758676460347653…19534699629914792961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.425 Γ— 10⁹¹(92-digit number)
24255517352920695307…39069399259829585921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.851 Γ— 10⁹¹(92-digit number)
48511034705841390615…78138798519659171841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.702 Γ— 10⁹¹(92-digit number)
97022069411682781230…56277597039318343681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.940 Γ— 10⁹²(93-digit number)
19404413882336556246…12555194078636687361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.880 Γ— 10⁹²(93-digit number)
38808827764673112492…25110388157273374721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.761 Γ— 10⁹²(93-digit number)
77617655529346224984…50220776314546749441
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 135731

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 bb7c2e8d8970b48a203ae9a750bbdeee2fb4da7cc24b9cef0dea172e61d5c215

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 #135,731 on Chainz β†—
Circulating Supply:57,857,687 XPMΒ·at block #6,826,691 Β· updates every 60s
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