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Home/Chain Registry/Block #3,268,188

Block #3,268,188

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/15/2019, 3:28:17 PM Β· Difficulty 10.9958 Β· 3,558,543 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e92bf0b2777fc11a0414b25699c6fc6388b809bc9b3965031a2f301bacb9bff9
View on Chainz β†—

Difficulty

10.995750

Transactions

1

Size

200 B

Version

2

Bits

0afee981

Nonce

1,193,148,134

Timestamp

7/15/2019, 3:28:17 PM

Confirmations

3,558,543

Merkle Root

eb70922d34c33d4940094d609a50709764cb79af0dfe7d664b4a7d70d9f689fc
Transactions (1)
Coinbaseeb70922d34c33d…4a7d70d9f689fc
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

6.949 Γ— 10⁹⁴(95-digit number)
69492130464452530535…15681099844180879520
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
6.949 Γ— 10⁹⁴(95-digit number)
69492130464452530535…15681099844180879519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.389 Γ— 10⁹⁡(96-digit number)
13898426092890506107…31362199688361759039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.779 Γ— 10⁹⁡(96-digit number)
27796852185781012214…62724399376723518079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.559 Γ— 10⁹⁡(96-digit number)
55593704371562024428…25448798753447036159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.111 Γ— 10⁹⁢(97-digit number)
11118740874312404885…50897597506894072319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.223 Γ— 10⁹⁢(97-digit number)
22237481748624809771…01795195013788144639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.447 Γ— 10⁹⁢(97-digit number)
44474963497249619542…03590390027576289279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.894 Γ— 10⁹⁢(97-digit number)
88949926994499239085…07180780055152578559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁷(98-digit number)
17789985398899847817…14361560110305157119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.557 Γ— 10⁹⁷(98-digit number)
35579970797799695634…28723120220610314239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.115 Γ— 10⁹⁷(98-digit number)
71159941595599391268…57446240441220628479
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 3268188

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 e92bf0b2777fc11a0414b25699c6fc6388b809bc9b3965031a2f301bacb9bff9

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 #3,268,188 on Chainz β†—
Circulating Supply:57,858,002 XPMΒ·at block #6,826,730 Β· updates every 60s
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