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Block #309,013

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2013, 9:34:36 AM Β· Difficulty 9.9947 Β· 6,491,254 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
de04471d94810a8aa774617c97695d89ccf7d0018912d4d75884e7eedbb59aff
View on Chainz β†—

Height

#309,013

Difficulty

9.994693

Transactions

1

Size

207 B

Version

2

Bits

09fea42d

Nonce

1,406

Timestamp

12/13/2013, 9:34:36 AM

Confirmations

6,491,254

Merkle Root

7d8457693399a9fce6dcdcc1459cae881f50f23f0eb5c44667acc09e1f1cd778
Transactions (1)
Coinbase7d8457693399a9…acc09e1f1cd778
1 in β†’ 1 out10.0000 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.

1.102 Γ— 10⁹⁢(97-digit number)
11022655710135241452…80481439981699363840
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
1.102 Γ— 10⁹⁢(97-digit number)
11022655710135241452…80481439981699363841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.204 Γ— 10⁹⁢(97-digit number)
22045311420270482904…60962879963398727681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.409 Γ— 10⁹⁢(97-digit number)
44090622840540965808…21925759926797455361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.818 Γ— 10⁹⁢(97-digit number)
88181245681081931616…43851519853594910721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.763 Γ— 10⁹⁷(98-digit number)
17636249136216386323…87703039707189821441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.527 Γ— 10⁹⁷(98-digit number)
35272498272432772646…75406079414379642881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.054 Γ— 10⁹⁷(98-digit number)
70544996544865545293…50812158828759285761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.410 Γ— 10⁹⁸(99-digit number)
14108999308973109058…01624317657518571521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.821 Γ— 10⁹⁸(99-digit number)
28217998617946218117…03248635315037143041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.643 Γ— 10⁹⁸(99-digit number)
56435997235892436234…06497270630074286081
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 309013

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 de04471d94810a8aa774617c97695d89ccf7d0018912d4d75884e7eedbb59aff

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 #309,013 on Chainz β†—
Circulating Supply:57,646,193 XPMΒ·at block #6,800,266 Β· updates every 60s
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