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Block #89,088

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/30/2013, 3:00:16 AM Β· Difficulty 9.2599 Β· 6,712,805 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a53d448a688fd5076889e09b03555a81d6e5156d425dc7e010eb75442dcbf815
View on Chainz β†—

Height

#89,088

Difficulty

9.259918

Transactions

1

Size

205 B

Version

2

Bits

09428a03

Nonce

17,525

Timestamp

7/30/2013, 3:00:16 AM

Confirmations

6,712,805

Merkle Root

43c86aad7e8e7911e599383669cb3f8d05c02a0f280dd725b99c02a6737deb61
Transactions (1)
Coinbase43c86aad7e8e79…9c02a6737deb61
1 in β†’ 1 out11.6500 XPM112 B
AT5A2KL6…CT16n6i2
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.

3.212 Γ— 10¹⁰¹(102-digit number)
32125393687466893858…98191704306453056800
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
3.212 Γ— 10¹⁰¹(102-digit number)
32125393687466893858…98191704306453056801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.425 Γ— 10¹⁰¹(102-digit number)
64250787374933787717…96383408612906113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.285 Γ— 10¹⁰²(103-digit number)
12850157474986757543…92766817225812227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.570 Γ— 10¹⁰²(103-digit number)
25700314949973515086…85533634451624454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.140 Γ— 10¹⁰²(103-digit number)
51400629899947030173…71067268903248908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.028 Γ— 10¹⁰³(104-digit number)
10280125979989406034…42134537806497817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.056 Γ— 10¹⁰³(104-digit number)
20560251959978812069…84269075612995635201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.112 Γ— 10¹⁰³(104-digit number)
41120503919957624139…68538151225991270401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.224 Γ— 10¹⁰³(104-digit number)
82241007839915248278…37076302451982540801
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 89088

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 a53d448a688fd5076889e09b03555a81d6e5156d425dc7e010eb75442dcbf815

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 #89,088 on Chainz β†—
Circulating Supply:57,659,235 XPMΒ·at block #6,801,892 Β· updates every 60s
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