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Block #277,969

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2013, 7:16:52 PM Β· Difficulty 9.9677 Β· 6,517,377 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
205f3797b6caf0983770e5f515aedc97f32ebd753ee723ba254a47ace76720bf
View on Chainz β†—

Height

#277,969

Difficulty

9.967672

Transactions

1

Size

201 B

Version

2

Bits

09f7b95b

Nonce

46,389

Timestamp

11/27/2013, 7:16:52 PM

Confirmations

6,517,377

Merkle Root

b5852f3e8cce3b3aeeba7407900740b0e2567d07e3fe75f11dfce96b1586683e
Transactions (1)
Coinbaseb5852f3e8cce3b…fce96b1586683e
1 in β†’ 1 out10.0500 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.347 Γ— 10⁹⁷(98-digit number)
23477359028181489829…61286184447016659180
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
2.347 Γ— 10⁹⁷(98-digit number)
23477359028181489829…61286184447016659181
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.695 Γ— 10⁹⁷(98-digit number)
46954718056362979658…22572368894033318361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.390 Γ— 10⁹⁷(98-digit number)
93909436112725959317…45144737788066636721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.878 Γ— 10⁹⁸(99-digit number)
18781887222545191863…90289475576133273441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.756 Γ— 10⁹⁸(99-digit number)
37563774445090383726…80578951152266546881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.512 Γ— 10⁹⁸(99-digit number)
75127548890180767453…61157902304533093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.502 Γ— 10⁹⁹(100-digit number)
15025509778036153490…22315804609066187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.005 Γ— 10⁹⁹(100-digit number)
30051019556072306981…44631609218132375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.010 Γ— 10⁹⁹(100-digit number)
60102039112144613963…89263218436264750081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.202 Γ— 10¹⁰⁰(101-digit number)
12020407822428922792…78526436872529500161
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 277969

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 205f3797b6caf0983770e5f515aedc97f32ebd753ee723ba254a47ace76720bf

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 #277,969 on Chainz β†—
Circulating Supply:57,606,821 XPMΒ·at block #6,795,345 Β· updates every 60s
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