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Block #245,615

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/5/2013, 2:14:50 PM Β· Difficulty 9.9640 Β· 6,554,593 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bea6b42262dc02025f0fc061d21e49e546b53f8fc97814bcd7befdc3fcb980c9
View on Chainz β†—

Height

#245,615

Difficulty

9.963955

Transactions

1

Size

206 B

Version

2

Bits

09f6c5c4

Nonce

66,343

Timestamp

11/5/2013, 2:14:50 PM

Confirmations

6,554,593

Merkle Root

78f719797dfe7a66687f29a916c09de3e8c5612aad5ba63790c38aedfb0db2ff
Transactions (1)
Coinbase78f719797dfe7a…c38aedfb0db2ff
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.491 Γ— 10⁹⁡(96-digit number)
14910157257485902378…99696083097406996800
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
1.491 Γ— 10⁹⁡(96-digit number)
14910157257485902378…99696083097406996801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.982 Γ— 10⁹⁡(96-digit number)
29820314514971804757…99392166194813993601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.964 Γ— 10⁹⁡(96-digit number)
59640629029943609514…98784332389627987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.192 Γ— 10⁹⁢(97-digit number)
11928125805988721902…97568664779255974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.385 Γ— 10⁹⁢(97-digit number)
23856251611977443805…95137329558511948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.771 Γ— 10⁹⁢(97-digit number)
47712503223954887611…90274659117023897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.542 Γ— 10⁹⁢(97-digit number)
95425006447909775222…80549318234047795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.908 Γ— 10⁹⁷(98-digit number)
19085001289581955044…61098636468095590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.817 Γ— 10⁹⁷(98-digit number)
38170002579163910089…22197272936191180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.634 Γ— 10⁹⁷(98-digit number)
76340005158327820178…44394545872382361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.526 Γ— 10⁹⁸(99-digit number)
15268001031665564035…88789091744764723201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 245615

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 bea6b42262dc02025f0fc061d21e49e546b53f8fc97814bcd7befdc3fcb980c9

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 #245,615 on Chainz β†—
Circulating Supply:57,645,735 XPMΒ·at block #6,800,207 Β· updates every 60s
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