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Block #2,570,513

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/17/2018, 1:03:37 PM Β· Difficulty 10.9944 Β· 4,273,292 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9bd85cd4d3a0a99ec7b616d8476df2f8d042843690f0c590e4a10f394c1bb160
View on Chainz β†—

Difficulty

10.994402

Transactions

1

Size

200 B

Version

2

Bits

0afe9124

Nonce

1,487,714,465

Timestamp

3/17/2018, 1:03:37 PM

Confirmations

4,273,292

Merkle Root

b62bcf8891c5f96e2a196625182597e16ea3d452ba88c89782dd265e2e65b9f3
Transactions (1)
Coinbaseb62bcf8891c5f9…dd265e2e65b9f3
1 in β†’ 1 out8.2600 XPM110 B
ASMZLnvr…UzusRrv6
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.

8.824 Γ— 10⁹³(94-digit number)
88241680351913111173…85663900294680152720
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
8.824 Γ— 10⁹³(94-digit number)
88241680351913111173…85663900294680152721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.764 Γ— 10⁹⁴(95-digit number)
17648336070382622234…71327800589360305441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.529 Γ— 10⁹⁴(95-digit number)
35296672140765244469…42655601178720610881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.059 Γ— 10⁹⁴(95-digit number)
70593344281530488938…85311202357441221761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.411 Γ— 10⁹⁡(96-digit number)
14118668856306097787…70622404714882443521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.823 Γ— 10⁹⁡(96-digit number)
28237337712612195575…41244809429764887041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.647 Γ— 10⁹⁡(96-digit number)
56474675425224391150…82489618859529774081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.129 Γ— 10⁹⁢(97-digit number)
11294935085044878230…64979237719059548161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.258 Γ— 10⁹⁢(97-digit number)
22589870170089756460…29958475438119096321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.517 Γ— 10⁹⁢(97-digit number)
45179740340179512920…59916950876238192641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.035 Γ— 10⁹⁢(97-digit number)
90359480680359025841…19833901752476385281
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 2570513

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 9bd85cd4d3a0a99ec7b616d8476df2f8d042843690f0c590e4a10f394c1bb160

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 #2,570,513 on Chainz β†—
Circulating Supply:57,994,814 XPMΒ·at block #6,843,804 Β· updates every 60s
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