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Block #1,050,115

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/8/2015, 8:28:01 AM Β· Difficulty 10.7278 Β· 5,764,371 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d9a76ea1d80d95e84408afd06dfda77d2a469f8fd2cfe002e1ac2d19ef2315d9
View on Chainz β†—

Difficulty

10.727846

Transactions

2

Size

433 B

Version

2

Bits

0aba5419

Nonce

142,269,477

Timestamp

5/8/2015, 8:28:01 AM

Confirmations

5,764,371

Merkle Root

90aacc0c4b7d09307c6f7a3c407caa03ec54e233790f735d81a00af104a953a2
Transactions (2)
Coinbasec2fa6b0ac5749d…3da619ca49f7e4
1 in β†’ 1 out8.6900 XPM116 B
ANSXnLY2…Sd25TjkD
c039b9b7e6a876…daf2547e5ca387
1 in β†’ 2 out1544.8800 XPM227 B
ANisw7ot…TLzK4jbrAWMLS7tj…cFhSAepm
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.

8.794 Γ— 10⁹⁡(96-digit number)
87947566943873194155…90027598147349087080
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
8.794 Γ— 10⁹⁡(96-digit number)
87947566943873194155…90027598147349087079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.758 Γ— 10⁹⁢(97-digit number)
17589513388774638831…80055196294698174159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.517 Γ— 10⁹⁢(97-digit number)
35179026777549277662…60110392589396348319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.035 Γ— 10⁹⁢(97-digit number)
70358053555098555324…20220785178792696639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.407 Γ— 10⁹⁷(98-digit number)
14071610711019711064…40441570357585393279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.814 Γ— 10⁹⁷(98-digit number)
28143221422039422129…80883140715170786559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.628 Γ— 10⁹⁷(98-digit number)
56286442844078844259…61766281430341573119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁸(99-digit number)
11257288568815768851…23532562860683146239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.251 Γ— 10⁹⁸(99-digit number)
22514577137631537703…47065125721366292479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.502 Γ— 10⁹⁸(99-digit number)
45029154275263075407…94130251442732584959
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 1050115

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 d9a76ea1d80d95e84408afd06dfda77d2a469f8fd2cfe002e1ac2d19ef2315d9

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 #1,050,115 on Chainz β†—
Circulating Supply:57,759,956 XPMΒ·at block #6,814,485 Β· updates every 60s
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