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Home/Chain Registry/Block #1,029,531

Block #1,029,531

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/23/2015, 2:48:55 PM Β· Difficulty 10.7594 Β· 5,797,452 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9ddce4e05c7b6a8761830924f88ea0677f576b4d4e04ddde7611971110a448e2
View on Chainz β†—

Difficulty

10.759407

Transactions

1

Size

206 B

Version

2

Bits

0ac26883

Nonce

73,165,499

Timestamp

4/23/2015, 2:48:55 PM

Confirmations

5,797,452

Merkle Root

b6e9f6f9389260306712ed6505b46cbc7ec0b16dbe35cbe1ea79b51589e854c2
Transactions (1)
Coinbaseb6e9f6f9389260…79b51589e854c2
1 in β†’ 1 out8.6200 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.

7.084 Γ— 10⁹⁡(96-digit number)
70846040541061030509…14503694311108864280
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
7.084 Γ— 10⁹⁡(96-digit number)
70846040541061030509…14503694311108864279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.416 Γ— 10⁹⁢(97-digit number)
14169208108212206101…29007388622217728559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.833 Γ— 10⁹⁢(97-digit number)
28338416216424412203…58014777244435457119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.667 Γ— 10⁹⁢(97-digit number)
56676832432848824407…16029554488870914239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.133 Γ— 10⁹⁷(98-digit number)
11335366486569764881…32059108977741828479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.267 Γ— 10⁹⁷(98-digit number)
22670732973139529763…64118217955483656959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.534 Γ— 10⁹⁷(98-digit number)
45341465946279059526…28236435910967313919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.068 Γ— 10⁹⁷(98-digit number)
90682931892558119052…56472871821934627839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.813 Γ— 10⁹⁸(99-digit number)
18136586378511623810…12945743643869255679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.627 Γ— 10⁹⁸(99-digit number)
36273172757023247621…25891487287738511359
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 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
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 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 1029531

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 9ddce4e05c7b6a8761830924f88ea0677f576b4d4e04ddde7611971110a448e2

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 #1,029,531 on Chainz β†—
Circulating Supply:57,860,038 XPMΒ·at block #6,826,982 Β· updates every 60s
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