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Block #89,156

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/30/2013, 4:08:09 AM Β· Difficulty 9.2600 Β· 6,707,437 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b01cdae8965dffeeb6f3e0a20a2cb2caef7a2dcd8afef6e2d65b81f76a103e5e
View on Chainz β†—

Height

#89,156

Difficulty

9.260009

Transactions

1

Size

201 B

Version

2

Bits

09428ffa

Nonce

165,103

Timestamp

7/30/2013, 4:08:09 AM

Confirmations

6,707,437

Merkle Root

ff1eea381f237c69084cf121c1017902d153ed21d497f02104a73feb21777108
Transactions (1)
Coinbaseff1eea381f237c…a73feb21777108
1 in β†’ 1 out11.6500 XPM109 B
AKFZhH2f…JBaegs5Q
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.

3.168 Γ— 10⁹⁹(100-digit number)
31689318140950867702…29793490329237022720
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
3.168 Γ— 10⁹⁹(100-digit number)
31689318140950867702…29793490329237022721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.337 Γ— 10⁹⁹(100-digit number)
63378636281901735405…59586980658474045441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.267 Γ— 10¹⁰⁰(101-digit number)
12675727256380347081…19173961316948090881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.535 Γ— 10¹⁰⁰(101-digit number)
25351454512760694162…38347922633896181761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.070 Γ— 10¹⁰⁰(101-digit number)
50702909025521388324…76695845267792363521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.014 Γ— 10¹⁰¹(102-digit number)
10140581805104277664…53391690535584727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.028 Γ— 10¹⁰¹(102-digit number)
20281163610208555329…06783381071169454081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.056 Γ— 10¹⁰¹(102-digit number)
40562327220417110659…13566762142338908161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.112 Γ— 10¹⁰¹(102-digit number)
81124654440834221318…27133524284677816321
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 89156

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 b01cdae8965dffeeb6f3e0a20a2cb2caef7a2dcd8afef6e2d65b81f76a103e5e

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 #89,156 on Chainz β†—
Circulating Supply:57,616,746 XPMΒ·at block #6,796,592 Β· updates every 60s
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