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Block #310,006

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2013, 9:06:37 PM Β· Difficulty 9.9950 Β· 6,488,133 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fce3e406ef0314f39b5fbd1a55e5d633f51d23d37d2e9abc3019368e5ea2b6e
View on Chainz β†—

Height

#310,006

Difficulty

9.995028

Transactions

1

Size

207 B

Version

2

Bits

09feba2a

Nonce

1,293

Timestamp

12/13/2013, 9:06:37 PM

Confirmations

6,488,133

Merkle Root

e5f423507981e2c09c8cf3a358c6dd28932f91fb9379acdce4dee8cff02e00cf
Transactions (1)
Coinbasee5f423507981e2…dee8cff02e00cf
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.

1.062 Γ— 10⁹⁷(98-digit number)
10624399732323309924…15737305642029159680
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
1.062 Γ— 10⁹⁷(98-digit number)
10624399732323309924…15737305642029159681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.124 Γ— 10⁹⁷(98-digit number)
21248799464646619849…31474611284058319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.249 Γ— 10⁹⁷(98-digit number)
42497598929293239698…62949222568116638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.499 Γ— 10⁹⁷(98-digit number)
84995197858586479397…25898445136233277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.699 Γ— 10⁹⁸(99-digit number)
16999039571717295879…51796890272466554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.399 Γ— 10⁹⁸(99-digit number)
33998079143434591759…03593780544933109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.799 Γ— 10⁹⁸(99-digit number)
67996158286869183518…07187561089866219521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.359 Γ— 10⁹⁹(100-digit number)
13599231657373836703…14375122179732439041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.719 Γ— 10⁹⁹(100-digit number)
27198463314747673407…28750244359464878081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.439 Γ— 10⁹⁹(100-digit number)
54396926629495346814…57500488718929756161
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 310006

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 2fce3e406ef0314f39b5fbd1a55e5d633f51d23d37d2e9abc3019368e5ea2b6e

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 #310,006 on Chainz β†—
Circulating Supply:57,629,111 XPMΒ·at block #6,798,138 Β· updates every 60s
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