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Block #2,527,425

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/18/2018, 7:31:50 PM Β· Difficulty 10.9841 Β· 4,312,999 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0fbbad9c622db19ebdebeeb4ac079b795a2d906f2decf253bf5c00da8c436560
View on Chainz β†—

Difficulty

10.984122

Transactions

1

Size

199 B

Version

2

Bits

0afbef6a

Nonce

1,961,378,975

Timestamp

2/18/2018, 7:31:50 PM

Confirmations

4,312,999

Merkle Root

f416ba321b5b9df77d29dbd002e664121d91ac13e71e795fff27b50fbd5747ab
Transactions (1)
Coinbasef416ba321b5b9d…27b50fbd5747ab
1 in β†’ 1 out8.2800 XPM110 B
AUhh5KUj…yF1RT5aW
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.

4.075 Γ— 10⁹³(94-digit number)
40754528725199773391…92657947080049631760
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
4.075 Γ— 10⁹³(94-digit number)
40754528725199773391…92657947080049631761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.150 Γ— 10⁹³(94-digit number)
81509057450399546782…85315894160099263521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.630 Γ— 10⁹⁴(95-digit number)
16301811490079909356…70631788320198527041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.260 Γ— 10⁹⁴(95-digit number)
32603622980159818712…41263576640397054081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.520 Γ— 10⁹⁴(95-digit number)
65207245960319637425…82527153280794108161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.304 Γ— 10⁹⁡(96-digit number)
13041449192063927485…65054306561588216321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.608 Γ— 10⁹⁡(96-digit number)
26082898384127854970…30108613123176432641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.216 Γ— 10⁹⁡(96-digit number)
52165796768255709940…60217226246352865281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.043 Γ— 10⁹⁢(97-digit number)
10433159353651141988…20434452492705730561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.086 Γ— 10⁹⁢(97-digit number)
20866318707302283976…40868904985411461121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.173 Γ— 10⁹⁢(97-digit number)
41732637414604567952…81737809970822922241
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 2527425

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 0fbbad9c622db19ebdebeeb4ac079b795a2d906f2decf253bf5c00da8c436560

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 #2,527,425 on Chainz β†—
Circulating Supply:57,967,717 XPMΒ·at block #6,840,423 Β· updates every 60s
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