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Home/Chain Registry/Block #2,301,281

Block #2,301,281

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/19/2017, 12:52:19 PM Β· Difficulty 10.9292 Β· 4,535,158 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6cc844f69feefff034aeca311ecf99d354d870446ea3f93d077c62351bb42a41
View on Chainz β†—

Difficulty

10.929169

Transactions

1

Size

200 B

Version

2

Bits

0aedde08

Nonce

1,505,823,817

Timestamp

9/19/2017, 12:52:19 PM

Confirmations

4,535,158

Merkle Root

7ddb8f29eff011f37d3971f544e618442a6c860d2aa2ae19bc61d050ac3ef3db
Transactions (1)
Coinbase7ddb8f29eff011…61d050ac3ef3db
1 in β†’ 1 out8.3600 XPM110 B
AR32FbeV…qbWS88Jg
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.

3.097 Γ— 10⁹⁴(95-digit number)
30974037565366057772…13642394043395539840
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
3.097 Γ— 10⁹⁴(95-digit number)
30974037565366057772…13642394043395539841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.194 Γ— 10⁹⁴(95-digit number)
61948075130732115545…27284788086791079681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.238 Γ— 10⁹⁡(96-digit number)
12389615026146423109…54569576173582159361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.477 Γ— 10⁹⁡(96-digit number)
24779230052292846218…09139152347164318721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.955 Γ— 10⁹⁡(96-digit number)
49558460104585692436…18278304694328637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.911 Γ— 10⁹⁡(96-digit number)
99116920209171384872…36556609388657274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.982 Γ— 10⁹⁢(97-digit number)
19823384041834276974…73113218777314549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.964 Γ— 10⁹⁢(97-digit number)
39646768083668553948…46226437554629099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.929 Γ— 10⁹⁢(97-digit number)
79293536167337107897…92452875109258199041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.585 Γ— 10⁹⁷(98-digit number)
15858707233467421579…84905750218516398081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.171 Γ— 10⁹⁷(98-digit number)
31717414466934843159…69811500437032796161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
6.343 Γ— 10⁹⁷(98-digit number)
63434828933869686318…39623000874065592321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the Second 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
ExceptionalChain length 12
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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2301281

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 6cc844f69feefff034aeca311ecf99d354d870446ea3f93d077c62351bb42a41

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 #2,301,281 on Chainz β†—
Circulating Supply:57,935,781 XPMΒ·at block #6,836,438 Β· updates every 60s
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