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Block #311,550

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/14/2013, 3:13:15 PM Β· Difficulty 9.9955 Β· 6,502,556 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b12c2e3beabef720809fed81a985df42f940f75578db2e92abda072a968f4b9a
View on Chainz β†—

Height

#311,550

Difficulty

9.995509

Transactions

1

Size

206 B

Version

2

Bits

09fed9a8

Nonce

51,478

Timestamp

12/14/2013, 3:13:15 PM

Confirmations

6,502,556

Merkle Root

36f44e99d2e7beddc0e7d45379b08a16eb6ea8a2b0c6acbc435266623fed96e6
Transactions (1)
Coinbase36f44e99d2e7be…5266623fed96e6
1 in β†’ 1 out9.9900 XPM116 B
AbwWkWZt…kawDhufa
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.

4.145 Γ— 10⁹³(94-digit number)
41456711927127663180…65682270133597259680
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
4.145 Γ— 10⁹³(94-digit number)
41456711927127663180…65682270133597259681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.291 Γ— 10⁹³(94-digit number)
82913423854255326360…31364540267194519361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.658 Γ— 10⁹⁴(95-digit number)
16582684770851065272…62729080534389038721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.316 Γ— 10⁹⁴(95-digit number)
33165369541702130544…25458161068778077441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.633 Γ— 10⁹⁴(95-digit number)
66330739083404261088…50916322137556154881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.326 Γ— 10⁹⁡(96-digit number)
13266147816680852217…01832644275112309761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.653 Γ— 10⁹⁡(96-digit number)
26532295633361704435…03665288550224619521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.306 Γ— 10⁹⁡(96-digit number)
53064591266723408870…07330577100449239041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.061 Γ— 10⁹⁢(97-digit number)
10612918253344681774…14661154200898478081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.122 Γ— 10⁹⁢(97-digit number)
21225836506689363548…29322308401796956161
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 311550

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 b12c2e3beabef720809fed81a985df42f940f75578db2e92abda072a968f4b9a

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 #311,550 on Chainz β†—
Circulating Supply:57,756,932 XPMΒ·at block #6,814,105 Β· updates every 60s
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