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Home/Chain Registry/Block #2,316,281

Block #2,316,281

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/30/2017, 8:29:17 PM Β· Difficulty 10.9088 Β· 4,525,535 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
26dbc0aa17c10c9e055b584634a37aecdd4bae04cf6383234f8bfee66942c3a0
View on Chainz β†—

Difficulty

10.908836

Transactions

1

Size

199 B

Version

2

Bits

0ae8a982

Nonce

399,570,063

Timestamp

9/30/2017, 8:29:17 PM

Confirmations

4,525,535

Merkle Root

a4abe39380078fec16da23e82e5a785744487036cc15365f321605ac2cf09fcf
Transactions (1)
Coinbasea4abe39380078f…1605ac2cf09fcf
1 in β†’ 1 out8.3900 XPM109 B
ASsjTXVY…oVVvQrpZ
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.

2.160 Γ— 10⁹⁴(95-digit number)
21606254497847484917…78961106869207019360
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
2.160 Γ— 10⁹⁴(95-digit number)
21606254497847484917…78961106869207019359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.321 Γ— 10⁹⁴(95-digit number)
43212508995694969835…57922213738414038719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.642 Γ— 10⁹⁴(95-digit number)
86425017991389939671…15844427476828077439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.728 Γ— 10⁹⁡(96-digit number)
17285003598277987934…31688854953656154879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.457 Γ— 10⁹⁡(96-digit number)
34570007196555975868…63377709907312309759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.914 Γ— 10⁹⁡(96-digit number)
69140014393111951737…26755419814624619519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁢(97-digit number)
13828002878622390347…53510839629249239039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.765 Γ— 10⁹⁢(97-digit number)
27656005757244780694…07021679258498478079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.531 Γ— 10⁹⁢(97-digit number)
55312011514489561389…14043358516996956159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.106 Γ— 10⁹⁷(98-digit number)
11062402302897912277…28086717033993912319
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 2316281

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 26dbc0aa17c10c9e055b584634a37aecdd4bae04cf6383234f8bfee66942c3a0

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 #2,316,281 on Chainz β†—
Circulating Supply:57,978,899 XPMΒ·at block #6,841,815 Β· updates every 60s
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