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Block #247,653

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/6/2013, 9:29:13 PM Β· Difficulty 9.9652 Β· 6,583,354 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5e5729153cad2b6c120b3e8413da3f80c6748ef3c5e226ea2dad20b3f6e1c970
View on Chainz β†—

Height

#247,653

Difficulty

9.965202

Transactions

1

Size

207 B

Version

2

Bits

09f7177d

Nonce

24,715

Timestamp

11/6/2013, 9:29:13 PM

Confirmations

6,583,354

Merkle Root

1ee99968285c3ccee70205c0839deae2ca370b6d09986ae7e71495ed7762f58e
Transactions (1)
Coinbase1ee99968285c3c…1495ed7762f58e
1 in β†’ 1 out10.0500 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.

1.114 Γ— 10⁹⁢(97-digit number)
11145501148317724814…93050786167464325120
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.114 Γ— 10⁹⁢(97-digit number)
11145501148317724814…93050786167464325119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.229 Γ— 10⁹⁢(97-digit number)
22291002296635449629…86101572334928650239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.458 Γ— 10⁹⁢(97-digit number)
44582004593270899258…72203144669857300479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.916 Γ— 10⁹⁢(97-digit number)
89164009186541798517…44406289339714600959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.783 Γ— 10⁹⁷(98-digit number)
17832801837308359703…88812578679429201919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.566 Γ— 10⁹⁷(98-digit number)
35665603674616719407…77625157358858403839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.133 Γ— 10⁹⁷(98-digit number)
71331207349233438814…55250314717716807679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.426 Γ— 10⁹⁸(99-digit number)
14266241469846687762…10500629435433615359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.853 Γ— 10⁹⁸(99-digit number)
28532482939693375525…21001258870867230719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.706 Γ— 10⁹⁸(99-digit number)
57064965879386751051…42002517741734461439
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 247653

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 5e5729153cad2b6c120b3e8413da3f80c6748ef3c5e226ea2dad20b3f6e1c970

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 #247,653 on Chainz β†—
Circulating Supply:57,892,198 XPMΒ·at block #6,831,006 Β· updates every 60s
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