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Block #251,169

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/8/2013, 9:15:48 PM Β· Difficulty 9.9695 Β· 6,581,950 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
21b17d4d015bcc470f68ce2b988fc43dd517c326ffb89eb84fa7a96310f1dea7
View on Chainz β†—

Height

#251,169

Difficulty

9.969534

Transactions

1

Size

228 B

Version

2

Bits

09f8335a

Nonce

7,011

Timestamp

11/8/2013, 9:15:48 PM

Confirmations

6,581,950

Merkle Root

082e34070141156278f1cddcc66c794b8d12ecddd20e4f873894ad9597ba71f7
Transactions (1)
Coinbase082e3407014115…94ad9597ba71f7
1 in β†’ 2 out10.0500 XPM137 B
AZDUEbdS…RYKMRZETASNt3cJa…L5zCqAYM
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.

3.216 Γ— 10⁹⁢(97-digit number)
32165541143558319962…00758743011017369600
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
3.216 Γ— 10⁹⁢(97-digit number)
32165541143558319962…00758743011017369601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.433 Γ— 10⁹⁢(97-digit number)
64331082287116639925…01517486022034739201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.286 Γ— 10⁹⁷(98-digit number)
12866216457423327985…03034972044069478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.573 Γ— 10⁹⁷(98-digit number)
25732432914846655970…06069944088138956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.146 Γ— 10⁹⁷(98-digit number)
51464865829693311940…12139888176277913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.029 Γ— 10⁹⁸(99-digit number)
10292973165938662388…24279776352555827201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.058 Γ— 10⁹⁸(99-digit number)
20585946331877324776…48559552705111654401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.117 Γ— 10⁹⁸(99-digit number)
41171892663754649552…97119105410223308801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.234 Γ— 10⁹⁸(99-digit number)
82343785327509299104…94238210820446617601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 251169

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 21b17d4d015bcc470f68ce2b988fc43dd517c326ffb89eb84fa7a96310f1dea7

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 #251,169 on Chainz β†—
Circulating Supply:57,909,128 XPMΒ·at block #6,833,118 Β· updates every 60s
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