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Home/Chain Registry/Block #2,069,418

Block #2,069,418

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/13/2017, 2:32:11 PM Β· Difficulty 10.8571 Β· 4,771,804 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d2560419a8c7659225e336f73220a0f4d9a72d64d637b2b4040ef48b6fbb3782
View on Chainz β†—

Difficulty

10.857114

Transactions

1

Size

200 B

Version

2

Bits

0adb6bd2

Nonce

50,967,698

Timestamp

4/13/2017, 2:32:11 PM

Confirmations

4,771,804

Merkle Root

c44d9c82158a0ec06bc5639146405fcf1af3878b7b816f6414e2364c3229097b
Transactions (1)
Coinbasec44d9c82158a0e…e2364c3229097b
1 in β†’ 1 out8.4700 XPM110 B
AM734h4B…eiHZ2bZs
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.

3.214 Γ— 10⁹⁴(95-digit number)
32146009247001706606…53703468927849950560
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
3.214 Γ— 10⁹⁴(95-digit number)
32146009247001706606…53703468927849950559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.429 Γ— 10⁹⁴(95-digit number)
64292018494003413213…07406937855699901119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.285 Γ— 10⁹⁡(96-digit number)
12858403698800682642…14813875711399802239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.571 Γ— 10⁹⁡(96-digit number)
25716807397601365285…29627751422799604479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.143 Γ— 10⁹⁡(96-digit number)
51433614795202730570…59255502845599208959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.028 Γ— 10⁹⁢(97-digit number)
10286722959040546114…18511005691198417919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.057 Γ— 10⁹⁢(97-digit number)
20573445918081092228…37022011382396835839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.114 Γ— 10⁹⁢(97-digit number)
41146891836162184456…74044022764793671679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.229 Γ— 10⁹⁢(97-digit number)
82293783672324368912…48088045529587343359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.645 Γ— 10⁹⁷(98-digit number)
16458756734464873782…96176091059174686719
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 2069418

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 d2560419a8c7659225e336f73220a0f4d9a72d64d637b2b4040ef48b6fbb3782

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 #2,069,418 on Chainz β†—
Circulating Supply:57,974,134 XPMΒ·at block #6,841,221 Β· updates every 60s
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