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Block #556,279

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/22/2014, 3:45:14 AM Β· Difficulty 10.9628 Β· 6,239,797 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d88407817caf80ca0bded4243c7756cea7578ca9a5f17f06caebe346f19f4cea
View on Chainz β†—

Height

#556,279

Difficulty

10.962812

Transactions

1

Size

207 B

Version

2

Bits

0af67ad8

Nonce

125,312,917

Timestamp

5/22/2014, 3:45:14 AM

Confirmations

6,239,797

Merkle Root

de38ec83ad635ca7ca6aae6e5fe51c752411ce1ceff82a1732a29e053f4ac94d
Transactions (1)
Coinbasede38ec83ad635c…a29e053f4ac94d
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.

5.105 Γ— 10⁹⁷(98-digit number)
51055434671898207380…21166678586865746550
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
5.105 Γ— 10⁹⁷(98-digit number)
51055434671898207380…21166678586865746549
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.021 Γ— 10⁹⁸(99-digit number)
10211086934379641476…42333357173731493099
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.042 Γ— 10⁹⁸(99-digit number)
20422173868759282952…84666714347462986199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.084 Γ— 10⁹⁸(99-digit number)
40844347737518565904…69333428694925972399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.168 Γ— 10⁹⁸(99-digit number)
81688695475037131808…38666857389851944799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.633 Γ— 10⁹⁹(100-digit number)
16337739095007426361…77333714779703889599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.267 Γ— 10⁹⁹(100-digit number)
32675478190014852723…54667429559407779199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.535 Γ— 10⁹⁹(100-digit number)
65350956380029705446…09334859118815558399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.307 Γ— 10¹⁰⁰(101-digit number)
13070191276005941089…18669718237631116799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.614 Γ— 10¹⁰⁰(101-digit number)
26140382552011882178…37339436475262233599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.228 Γ— 10¹⁰⁰(101-digit number)
52280765104023764357…74678872950524467199
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 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
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 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 556279

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 d88407817caf80ca0bded4243c7756cea7578ca9a5f17f06caebe346f19f4cea

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 #556,279 on Chainz β†—
Circulating Supply:57,612,704 XPMΒ·at block #6,796,075 Β· updates every 60s
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