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Block #1,598,598

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2016, 9:26:42 PM Β· Difficulty 10.6106 Β· 5,226,031 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
acca147cbac35db0bd1a900ed4aa96f7dfc03417e675b50aa9e0d8d164cbce9a
View on Chainz β†—

Difficulty

10.610610

Transactions

1

Size

199 B

Version

2

Bits

0a9c50f1

Nonce

773,818,070

Timestamp

5/24/2016, 9:26:42 PM

Confirmations

5,226,031

Merkle Root

4d236f24f35a1c93c161cf23d6335b869fa3af2d25d81551ec9f42de5cb2714a
Transactions (1)
Coinbase4d236f24f35a1c…9f42de5cb2714a
1 in β†’ 1 out8.8700 XPM109 B
ANVc1hDu…V9uXi6h8
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.

6.664 Γ— 10⁹⁡(96-digit number)
66642267581352873104…21562967849402839040
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
6.664 Γ— 10⁹⁡(96-digit number)
66642267581352873104…21562967849402839041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.332 Γ— 10⁹⁢(97-digit number)
13328453516270574620…43125935698805678081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.665 Γ— 10⁹⁢(97-digit number)
26656907032541149241…86251871397611356161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.331 Γ— 10⁹⁢(97-digit number)
53313814065082298483…72503742795222712321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.066 Γ— 10⁹⁷(98-digit number)
10662762813016459696…45007485590445424641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.132 Γ— 10⁹⁷(98-digit number)
21325525626032919393…90014971180890849281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.265 Γ— 10⁹⁷(98-digit number)
42651051252065838786…80029942361781698561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.530 Γ— 10⁹⁷(98-digit number)
85302102504131677573…60059884723563397121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.706 Γ— 10⁹⁸(99-digit number)
17060420500826335514…20119769447126794241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.412 Γ— 10⁹⁸(99-digit number)
34120841001652671029…40239538894253588481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1598598

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 acca147cbac35db0bd1a900ed4aa96f7dfc03417e675b50aa9e0d8d164cbce9a

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 #1,598,598 on Chainz β†—
Circulating Supply:57,841,095 XPMΒ·at block #6,824,628 Β· updates every 60s
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