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Block #536,258

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/11/2014, 8:24:20 AM Β· Difficulty 10.9086 Β· 6,301,457 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a272f2a93a6a5aee438a33b6137cc2319e280b272ec52b77df278dc1b3d7f945
View on Chainz β†—

Height

#536,258

Difficulty

10.908644

Transactions

1

Size

201 B

Version

2

Bits

0ae89ce0

Nonce

126,182,073

Timestamp

5/11/2014, 8:24:20 AM

Confirmations

6,301,457

Merkle Root

7ceee2dab9c34c1d43ce8e7d8645267be30ee2429f7805a3f20cb383bcf0f0a4
Transactions (1)
Coinbase7ceee2dab9c34c…0cb383bcf0f0a4
1 in β†’ 1 out8.3900 XPM110 B
AYmMbuk6…WSrMQxBn
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.

2.376 Γ— 10⁹⁷(98-digit number)
23764778992341172169…40285195177669268320
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
2.376 Γ— 10⁹⁷(98-digit number)
23764778992341172169…40285195177669268321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.752 Γ— 10⁹⁷(98-digit number)
47529557984682344338…80570390355338536641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.505 Γ— 10⁹⁷(98-digit number)
95059115969364688677…61140780710677073281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.901 Γ— 10⁹⁸(99-digit number)
19011823193872937735…22281561421354146561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.802 Γ— 10⁹⁸(99-digit number)
38023646387745875470…44563122842708293121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.604 Γ— 10⁹⁸(99-digit number)
76047292775491750941…89126245685416586241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.520 Γ— 10⁹⁹(100-digit number)
15209458555098350188…78252491370833172481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.041 Γ— 10⁹⁹(100-digit number)
30418917110196700376…56504982741666344961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.083 Γ— 10⁹⁹(100-digit number)
60837834220393400753…13009965483332689921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.216 Γ— 10¹⁰⁰(101-digit number)
12167566844078680150…26019930966665379841
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 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
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 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 536258

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 a272f2a93a6a5aee438a33b6137cc2319e280b272ec52b77df278dc1b3d7f945

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 #536,258 on Chainz β†—
Circulating Supply:57,946,048 XPMΒ·at block #6,837,714 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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