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Block #247,283

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/6/2013, 4:10:34 PM Β· Difficulty 9.9648 Β· 6,548,410 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
50737a06dd70139db884d783e03a3e8c1a58737f0e1555d4194959391cfb7227
View on Chainz β†—

Height

#247,283

Difficulty

9.964831

Transactions

1

Size

207 B

Version

2

Bits

09f6ff24

Nonce

47,463

Timestamp

11/6/2013, 4:10:34 PM

Confirmations

6,548,410

Merkle Root

e309aa3f9e3b61eb4fa0d0699146afa90ad079d66e8829041a08309a3ae68dbc
Transactions (1)
Coinbasee309aa3f9e3b61…08309a3ae68dbc
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.136 Γ— 10⁹⁢(97-digit number)
21369881698395261422…75968634526635788800
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
2.136 Γ— 10⁹⁢(97-digit number)
21369881698395261422…75968634526635788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.273 Γ— 10⁹⁢(97-digit number)
42739763396790522845…51937269053271577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.547 Γ— 10⁹⁢(97-digit number)
85479526793581045691…03874538106543155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.709 Γ— 10⁹⁷(98-digit number)
17095905358716209138…07749076213086310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.419 Γ— 10⁹⁷(98-digit number)
34191810717432418276…15498152426172620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.838 Γ— 10⁹⁷(98-digit number)
68383621434864836553…30996304852345241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.367 Γ— 10⁹⁸(99-digit number)
13676724286972967310…61992609704690483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.735 Γ— 10⁹⁸(99-digit number)
27353448573945934621…23985219409380966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.470 Γ— 10⁹⁸(99-digit number)
54706897147891869242…47970438818761932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.094 Γ— 10⁹⁹(100-digit number)
10941379429578373848…95940877637523865601
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 247283

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 50737a06dd70139db884d783e03a3e8c1a58737f0e1555d4194959391cfb7227

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 #247,283 on Chainz β†—
Circulating Supply:57,609,614 XPMΒ·at block #6,795,692 Β· updates every 60s
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