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Block #1,692,311

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/28/2016, 6:44:36 AM Β· Difficulty 10.6840 Β· 5,140,661 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cdf73feb98db84aa724ca646189577dd78655633473132ad7f3d28c7d0048089
View on Chainz β†—

Difficulty

10.684018

Transactions

1

Size

201 B

Version

2

Bits

0aaf1bcb

Nonce

62,450,493

Timestamp

7/28/2016, 6:44:36 AM

Confirmations

5,140,661

Merkle Root

e4e53cdb5ba4b5705f5021bf41f3739040093662b09a87cb72925d75afa3c4c3
Transactions (1)
Coinbasee4e53cdb5ba4b5…925d75afa3c4c3
1 in β†’ 1 out8.7500 XPM110 B
APYfxocf…7ENDSh9f
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.

1.732 Γ— 10⁹⁢(97-digit number)
17322328383174184967…38274011887218524160
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
1.732 Γ— 10⁹⁢(97-digit number)
17322328383174184967…38274011887218524159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.464 Γ— 10⁹⁢(97-digit number)
34644656766348369934…76548023774437048319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.928 Γ— 10⁹⁢(97-digit number)
69289313532696739869…53096047548874096639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.385 Γ— 10⁹⁷(98-digit number)
13857862706539347973…06192095097748193279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.771 Γ— 10⁹⁷(98-digit number)
27715725413078695947…12384190195496386559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.543 Γ— 10⁹⁷(98-digit number)
55431450826157391895…24768380390992773119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.108 Γ— 10⁹⁸(99-digit number)
11086290165231478379…49536760781985546239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.217 Γ— 10⁹⁸(99-digit number)
22172580330462956758…99073521563971092479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.434 Γ— 10⁹⁸(99-digit number)
44345160660925913516…98147043127942184959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.869 Γ— 10⁹⁸(99-digit number)
88690321321851827033…96294086255884369919
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 1692311

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 cdf73feb98db84aa724ca646189577dd78655633473132ad7f3d28c7d0048089

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 #1,692,311 on Chainz β†—
Circulating Supply:57,907,954 XPMΒ·at block #6,832,971 Β· updates every 60s
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