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Block #36,598

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 9:35:38 AM Β· Difficulty 7.9955 Β· 6,768,555 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a94904eb2cf6c9e89bf3dbf43a1c0eadde3ca247deb4fcc2034765e4cd1d2cba
View on Chainz β†—

Height

#36,598

Difficulty

7.995516

Transactions

1

Size

198 B

Version

2

Bits

07feda1b

Nonce

841

Timestamp

7/14/2013, 9:35:38 AM

Confirmations

6,768,555

Merkle Root

33d9cf2981078b870c2561cacb49bac402147b1fa9056a5e8efd2d6f746ee0c4
Transactions (1)
Coinbase33d9cf2981078b…fd2d6f746ee0c4
1 in β†’ 1 out15.6200 XPM109 B
ANcWPyFX…whZcn7hZ
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.

2.570 Γ— 10⁹³(94-digit number)
25705943478097407150…88704518710030893600
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.570 Γ— 10⁹³(94-digit number)
25705943478097407150…88704518710030893599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.141 Γ— 10⁹³(94-digit number)
51411886956194814301…77409037420061787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁴(95-digit number)
10282377391238962860…54818074840123574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.056 Γ— 10⁹⁴(95-digit number)
20564754782477925720…09636149680247148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.112 Γ— 10⁹⁴(95-digit number)
41129509564955851441…19272299360494297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.225 Γ— 10⁹⁴(95-digit number)
82259019129911702882…38544598720988595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.645 Γ— 10⁹⁡(96-digit number)
16451803825982340576…77089197441977190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.290 Γ— 10⁹⁡(96-digit number)
32903607651964681153…54178394883954380799
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 36598

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 a94904eb2cf6c9e89bf3dbf43a1c0eadde3ca247deb4fcc2034765e4cd1d2cba

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 #36,598 on Chainz β†—
Circulating Supply:57,685,291 XPMΒ·at block #6,805,152 Β· updates every 60s
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