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Block #553,568

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/20/2014, 5:58:49 AM Β· Difficulty 10.9630 Β· 6,258,779 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8fec5e2a46bfbfc25f9f43acd53a1b8b52fc45fd7db11e1bf4adc9a5f2f56a31
View on Chainz β†—

Height

#553,568

Difficulty

10.962985

Transactions

1

Size

208 B

Version

2

Bits

0af6862f

Nonce

1,739,877,483

Timestamp

5/20/2014, 5:58:49 AM

Confirmations

6,258,779

Merkle Root

1172d218815a4e6abdbe57b0a68cf8a15a7f8e5f1f61c2efb3792c248bebcbf3
Transactions (1)
Coinbase1172d218815a4e…792c248bebcbf3
1 in β†’ 1 out8.3100 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.

5.538 Γ— 10⁹⁸(99-digit number)
55389896938949275928…35662235109938444640
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
5.538 Γ— 10⁹⁸(99-digit number)
55389896938949275928…35662235109938444641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.107 Γ— 10⁹⁹(100-digit number)
11077979387789855185…71324470219876889281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.215 Γ— 10⁹⁹(100-digit number)
22155958775579710371…42648940439753778561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.431 Γ— 10⁹⁹(100-digit number)
44311917551159420742…85297880879507557121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.862 Γ— 10⁹⁹(100-digit number)
88623835102318841485…70595761759015114241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.772 Γ— 10¹⁰⁰(101-digit number)
17724767020463768297…41191523518030228481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.544 Γ— 10¹⁰⁰(101-digit number)
35449534040927536594…82383047036060456961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.089 Γ— 10¹⁰⁰(101-digit number)
70899068081855073188…64766094072120913921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.417 Γ— 10¹⁰¹(102-digit number)
14179813616371014637…29532188144241827841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.835 Γ— 10¹⁰¹(102-digit number)
28359627232742029275…59064376288483655681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.671 Γ— 10¹⁰¹(102-digit number)
56719254465484058550…18128752576967311361
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 553568

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 8fec5e2a46bfbfc25f9f43acd53a1b8b52fc45fd7db11e1bf4adc9a5f2f56a31

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 #553,568 on Chainz β†—
Circulating Supply:57,742,796 XPMΒ·at block #6,812,346 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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