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Block #654,997

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/30/2014, 2:05:57 PM Β· Difficulty 10.9555 Β· 6,161,906 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76f4e2ae6734ebb5dc110b17d852cea6c383341a644c8d42672cc34cba988682
View on Chainz β†—

Height

#654,997

Difficulty

10.955510

Transactions

1

Size

207 B

Version

2

Bits

0af49c56

Nonce

85,654,404

Timestamp

7/30/2014, 2:05:57 PM

Confirmations

6,161,906

Merkle Root

6b4d4a9655b341a00f8eeb3016313d2218b774e056b96c1c0096f816fd7c15e3
Transactions (1)
Coinbase6b4d4a9655b341…96f816fd7c15e3
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

5.351 Γ— 10⁹⁷(98-digit number)
53519858289835385032…74846249824125696000
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
5.351 Γ— 10⁹⁷(98-digit number)
53519858289835385032…74846249824125696001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.070 Γ— 10⁹⁸(99-digit number)
10703971657967077006…49692499648251392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.140 Γ— 10⁹⁸(99-digit number)
21407943315934154013…99384999296502784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.281 Γ— 10⁹⁸(99-digit number)
42815886631868308026…98769998593005568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.563 Γ— 10⁹⁸(99-digit number)
85631773263736616052…97539997186011136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.712 Γ— 10⁹⁹(100-digit number)
17126354652747323210…95079994372022272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.425 Γ— 10⁹⁹(100-digit number)
34252709305494646421…90159988744044544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.850 Γ— 10⁹⁹(100-digit number)
68505418610989292842…80319977488089088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.370 Γ— 10¹⁰⁰(101-digit number)
13701083722197858568…60639954976178176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.740 Γ— 10¹⁰⁰(101-digit number)
27402167444395717136…21279909952356352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.480 Γ— 10¹⁰⁰(101-digit number)
54804334888791434273…42559819904712704001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 654997

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 76f4e2ae6734ebb5dc110b17d852cea6c383341a644c8d42672cc34cba988682

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 #654,997 on Chainz β†—
Circulating Supply:57,779,264 XPMΒ·at block #6,816,902 Β· updates every 60s
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