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Block #534,573

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/10/2014, 9:58:59 AM Β· Difficulty 10.9022 Β· 6,282,300 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
821ef2c8350cf0e09d76fd4c3eeea84f37f5c75320850148c43334afd3d27e52
View on Chainz β†—

Height

#534,573

Difficulty

10.902205

Transactions

1

Size

208 B

Version

2

Bits

0ae6f6e7

Nonce

97,940,974

Timestamp

5/10/2014, 9:58:59 AM

Confirmations

6,282,300

Merkle Root

d85a45a80f3ee7bf964edd52e7412ee885f88ca1cf9df53d88f3251c1a7c3afd
Transactions (1)
Coinbased85a45a80f3ee7…f3251c1a7c3afd
1 in β†’ 1 out8.4000 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.

2.677 Γ— 10⁹⁹(100-digit number)
26777598234331841768…75628269571345495360
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
2.677 Γ— 10⁹⁹(100-digit number)
26777598234331841768…75628269571345495359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.355 Γ— 10⁹⁹(100-digit number)
53555196468663683537…51256539142690990719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.071 Γ— 10¹⁰⁰(101-digit number)
10711039293732736707…02513078285381981439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.142 Γ— 10¹⁰⁰(101-digit number)
21422078587465473414…05026156570763962879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.284 Γ— 10¹⁰⁰(101-digit number)
42844157174930946829…10052313141527925759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.568 Γ— 10¹⁰⁰(101-digit number)
85688314349861893659…20104626283055851519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.713 Γ— 10¹⁰¹(102-digit number)
17137662869972378731…40209252566111703039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.427 Γ— 10¹⁰¹(102-digit number)
34275325739944757463…80418505132223406079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.855 Γ— 10¹⁰¹(102-digit number)
68550651479889514927…60837010264446812159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.371 Γ— 10¹⁰²(103-digit number)
13710130295977902985…21674020528893624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.742 Γ— 10¹⁰²(103-digit number)
27420260591955805970…43348041057787248639
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 534573

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 821ef2c8350cf0e09d76fd4c3eeea84f37f5c75320850148c43334afd3d27e52

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 #534,573 on Chainz β†—
Circulating Supply:57,779,022 XPMΒ·at block #6,816,872 Β· updates every 60s
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