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Home/Chain Registry/Block #2,486,103

Block #2,486,103

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/23/2018, 9:09:15 AM Β· Difficulty 10.9679 Β· 4,355,641 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1b9bbedba9060be494794848f18c7e521d28d1b362be43e254f6ebac32aa0677
View on Chainz β†—

Difficulty

10.967946

Transactions

1

Size

201 B

Version

2

Bits

0af7cb4c

Nonce

928,659,029

Timestamp

1/23/2018, 9:09:15 AM

Confirmations

4,355,641

Merkle Root

ef2b4185dc93983f2891a015e116e7b4d15d1bdc593e8f9c9833b763193f962c
Transactions (1)
Coinbaseef2b4185dc9398…33b763193f962c
1 in β†’ 1 out8.3000 XPM110 B
AQe5WDHw…nvzJtoyx
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.

2.275 Γ— 10⁹⁢(97-digit number)
22753059625969179436…13057099156401863680
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
2.275 Γ— 10⁹⁢(97-digit number)
22753059625969179436…13057099156401863679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.550 Γ— 10⁹⁢(97-digit number)
45506119251938358873…26114198312803727359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.101 Γ— 10⁹⁢(97-digit number)
91012238503876717747…52228396625607454719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.820 Γ— 10⁹⁷(98-digit number)
18202447700775343549…04456793251214909439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.640 Γ— 10⁹⁷(98-digit number)
36404895401550687099…08913586502429818879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.280 Γ— 10⁹⁷(98-digit number)
72809790803101374198…17827173004859637759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.456 Γ— 10⁹⁸(99-digit number)
14561958160620274839…35654346009719275519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.912 Γ— 10⁹⁸(99-digit number)
29123916321240549679…71308692019438551039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.824 Γ— 10⁹⁸(99-digit number)
58247832642481099358…42617384038877102079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.164 Γ— 10⁹⁹(100-digit number)
11649566528496219871…85234768077754204159
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 2486103

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 1b9bbedba9060be494794848f18c7e521d28d1b362be43e254f6ebac32aa0677

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 #2,486,103 on Chainz β†—
Circulating Supply:57,978,336 XPMΒ·at block #6,841,743 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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