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Home/Chain Registry/Block #2,815,273

Block #2,815,273

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2018, 12:13:44 PM Β· Difficulty 11.6831 Β· 4,026,605 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e9f64a489189b338960dbef4a9239ca1c8edc96032cb691d56d4e93b912a9b34
View on Chainz β†—

Difficulty

11.683060

Transactions

1

Size

200 B

Version

2

Bits

0baedd05

Nonce

247,498,313

Timestamp

8/29/2018, 12:13:44 PM

Confirmations

4,026,605

Merkle Root

0b88e1ad576eb7ee1d8ffc08663faca3639d34b2fcea4dd2f7a45061408219a9
Transactions (1)
Coinbase0b88e1ad576eb7…a45061408219a9
1 in β†’ 1 out7.3100 XPM110 B
AZemPr8n…HCsAk1qy
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.

7.515 Γ— 10⁹³(94-digit number)
75154468777606602942…08721411717988763360
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
7.515 Γ— 10⁹³(94-digit number)
75154468777606602942…08721411717988763361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.503 Γ— 10⁹⁴(95-digit number)
15030893755521320588…17442823435977526721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.006 Γ— 10⁹⁴(95-digit number)
30061787511042641176…34885646871955053441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.012 Γ— 10⁹⁴(95-digit number)
60123575022085282353…69771293743910106881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.202 Γ— 10⁹⁡(96-digit number)
12024715004417056470…39542587487820213761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.404 Γ— 10⁹⁡(96-digit number)
24049430008834112941…79085174975640427521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.809 Γ— 10⁹⁡(96-digit number)
48098860017668225882…58170349951280855041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.619 Γ— 10⁹⁡(96-digit number)
96197720035336451765…16340699902561710081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.923 Γ— 10⁹⁢(97-digit number)
19239544007067290353…32681399805123420161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.847 Γ— 10⁹⁢(97-digit number)
38479088014134580706…65362799610246840321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.695 Γ— 10⁹⁢(97-digit number)
76958176028269161412…30725599220493680641
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 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
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 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 2815273

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 e9f64a489189b338960dbef4a9239ca1c8edc96032cb691d56d4e93b912a9b34

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 #2,815,273 on Chainz β†—
Circulating Supply:57,979,400 XPMΒ·at block #6,841,877 Β· updates every 60s
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