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Home/Chain Registry/Block #2,098,602

Block #2,098,602

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2017, 6:09:05 PM Β· Difficulty 10.8627 Β· 4,734,411 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8d14f658f9e4385a578420359cd1bfe777dcc0d324690a6bf209e75029b81a22
View on Chainz β†—

Difficulty

10.862730

Transactions

1

Size

199 B

Version

2

Bits

0adcdbe3

Nonce

350,484,303

Timestamp

5/3/2017, 6:09:05 PM

Confirmations

4,734,411

Merkle Root

9d37f7b7e2ef794464f828c205625509a0edf33c6879f22ec23c6249346df567
Transactions (1)
Coinbase9d37f7b7e2ef79…3c6249346df567
1 in β†’ 1 out8.4600 XPM109 B
AKWb3Set…KMcT9Coh
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.

5.040 Γ— 10⁹⁴(95-digit number)
50402079916555289848…81158974833896716800
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
5.040 Γ— 10⁹⁴(95-digit number)
50402079916555289848…81158974833896716799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁡(96-digit number)
10080415983311057969…62317949667793433599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.016 Γ— 10⁹⁡(96-digit number)
20160831966622115939…24635899335586867199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.032 Γ— 10⁹⁡(96-digit number)
40321663933244231879…49271798671173734399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.064 Γ— 10⁹⁡(96-digit number)
80643327866488463758…98543597342347468799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.612 Γ— 10⁹⁢(97-digit number)
16128665573297692751…97087194684694937599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.225 Γ— 10⁹⁢(97-digit number)
32257331146595385503…94174389369389875199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.451 Γ— 10⁹⁢(97-digit number)
64514662293190771006…88348778738779750399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.290 Γ— 10⁹⁷(98-digit number)
12902932458638154201…76697557477559500799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.580 Γ— 10⁹⁷(98-digit number)
25805864917276308402…53395114955119001599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.161 Γ— 10⁹⁷(98-digit number)
51611729834552616805…06790229910238003199
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 2098602

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 8d14f658f9e4385a578420359cd1bfe777dcc0d324690a6bf209e75029b81a22

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 #2,098,602 on Chainz β†—
Circulating Supply:57,908,279 XPMΒ·at block #6,833,012 Β· updates every 60s
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