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Block #30,596

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 7:53:18 PM Β· Difficulty 7.9872 Β· 6,781,118 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
34b32c04b987074804deee8f3a47bc218f71a21645805770d78e73e0d66c2fc5
View on Chainz β†—

Height

#30,596

Difficulty

7.987161

Transactions

1

Size

199 B

Version

2

Bits

07fcb694

Nonce

1,264

Timestamp

7/13/2013, 7:53:18 PM

Confirmations

6,781,118

Merkle Root

65977f2ab94103e631f5c218a0ed644ed4e4dd7d6432ee1f8c0630ab0ef169b5
Transactions (1)
Coinbase65977f2ab94103…0630ab0ef169b5
1 in β†’ 1 out15.6500 XPM108 B
Ae78mnnm…cgtMTozr
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.

5.561 Γ— 10⁹⁷(98-digit number)
55619548256707041949…99809512877935282140
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
5.561 Γ— 10⁹⁷(98-digit number)
55619548256707041949…99809512877935282141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.112 Γ— 10⁹⁸(99-digit number)
11123909651341408389…99619025755870564281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.224 Γ— 10⁹⁸(99-digit number)
22247819302682816779…99238051511741128561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.449 Γ— 10⁹⁸(99-digit number)
44495638605365633559…98476103023482257121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.899 Γ— 10⁹⁸(99-digit number)
88991277210731267119…96952206046964514241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.779 Γ— 10⁹⁹(100-digit number)
17798255442146253423…93904412093929028481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.559 Γ— 10⁹⁹(100-digit number)
35596510884292506847…87808824187858056961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.119 Γ— 10⁹⁹(100-digit number)
71193021768585013695…75617648375716113921
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8
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 30596

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 34b32c04b987074804deee8f3a47bc218f71a21645805770d78e73e0d66c2fc5

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 #30,596 on Chainz β†—
Circulating Supply:57,737,824 XPMΒ·at block #6,811,713 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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