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Block #273,197

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2013, 4:27:33 PM Β· Difficulty 9.9543 Β· 6,527,608 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c22007e4ec3da4ce3d1be5028a0c2c694abc88f3b14387566bf7c11ba3e602f3
View on Chainz β†—

Height

#273,197

Difficulty

9.954305

Transactions

1

Size

207 B

Version

2

Bits

09f44d54

Nonce

33,555,428

Timestamp

11/25/2013, 4:27:33 PM

Confirmations

6,527,608

Merkle Root

4f8f2114b90bd73de7fbc60eb9130cfdaaac7f90cc0b9d047c9faa172215a6bd
Transactions (1)
Coinbase4f8f2114b90bd7…9faa172215a6bd
1 in β†’ 1 out10.0800 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.

2.670 Γ— 10⁹⁢(97-digit number)
26707289210241439691…02157745044811331840
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
2.670 Γ— 10⁹⁢(97-digit number)
26707289210241439691…02157745044811331841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.341 Γ— 10⁹⁢(97-digit number)
53414578420482879382…04315490089622663681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.068 Γ— 10⁹⁷(98-digit number)
10682915684096575876…08630980179245327361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.136 Γ— 10⁹⁷(98-digit number)
21365831368193151752…17261960358490654721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.273 Γ— 10⁹⁷(98-digit number)
42731662736386303505…34523920716981309441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.546 Γ— 10⁹⁷(98-digit number)
85463325472772607011…69047841433962618881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.709 Γ— 10⁹⁸(99-digit number)
17092665094554521402…38095682867925237761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.418 Γ— 10⁹⁸(99-digit number)
34185330189109042804…76191365735850475521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.837 Γ— 10⁹⁸(99-digit number)
68370660378218085609…52382731471700951041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.367 Γ— 10⁹⁹(100-digit number)
13674132075643617121…04765462943401902081
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 273197

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 c22007e4ec3da4ce3d1be5028a0c2c694abc88f3b14387566bf7c11ba3e602f3

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 #273,197 on Chainz β†—
Circulating Supply:57,650,493 XPMΒ·at block #6,800,804 Β· updates every 60s
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