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Block #272,183

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2013, 2:48:46 AM Β· Difficulty 9.9525 Β· 6,524,000 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
09d0c1c11f9f50c79a24d48dcd21727616cfaec59c23d7bbc3d8ef216b8f6d80
View on Chainz β†—

Height

#272,183

Difficulty

9.952461

Transactions

1

Size

209 B

Version

2

Bits

09f3d47a

Nonce

22,621

Timestamp

11/25/2013, 2:48:46 AM

Confirmations

6,524,000

Merkle Root

0339321e541dcafcd5629b8a9a50ba2cb20d12a066322cb412b0ac088168a4e2
Transactions (1)
Coinbase0339321e541dca…b0ac088168a4e2
1 in β†’ 1 out10.0800 XPM118 B
AZxPvBWY…e18sa12g
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.

5.879 Γ— 10⁹⁢(97-digit number)
58798738270480585268…36863509329778699000
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
5.879 Γ— 10⁹⁢(97-digit number)
58798738270480585268…36863509329778699001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.175 Γ— 10⁹⁷(98-digit number)
11759747654096117053…73727018659557398001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.351 Γ— 10⁹⁷(98-digit number)
23519495308192234107…47454037319114796001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.703 Γ— 10⁹⁷(98-digit number)
47038990616384468214…94908074638229592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.407 Γ— 10⁹⁷(98-digit number)
94077981232768936429…89816149276459184001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.881 Γ— 10⁹⁸(99-digit number)
18815596246553787285…79632298552918368001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.763 Γ— 10⁹⁸(99-digit number)
37631192493107574571…59264597105836736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.526 Γ— 10⁹⁸(99-digit number)
75262384986215149143…18529194211673472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.505 Γ— 10⁹⁹(100-digit number)
15052476997243029828…37058388423346944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.010 Γ— 10⁹⁹(100-digit number)
30104953994486059657…74116776846693888001
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 272183

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 09d0c1c11f9f50c79a24d48dcd21727616cfaec59c23d7bbc3d8ef216b8f6d80

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 #272,183 on Chainz β†—
Circulating Supply:57,613,462 XPMΒ·at block #6,796,182 Β· updates every 60s
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