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Block #264,957

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2013, 3:40:34 AM Β· Difficulty 9.9635 Β· 6,535,465 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb7cbea2a3028e97124d16c8e2b42839bd965a30ab8a101e0557a9bc97ce782e
View on Chainz β†—

Height

#264,957

Difficulty

9.963499

Transactions

2

Size

867 B

Version

2

Bits

09f6a7e7

Nonce

33,555

Timestamp

11/19/2013, 3:40:34 AM

Confirmations

6,535,465

Merkle Root

433dabbecc6cd1ee10fac4ad466d71194af55daf5078a5a5826e0d275fbb5f54
Transactions (2)
Coinbase6a4e7d8f2b5566…a5cd19fc0565b8
1 in β†’ 1 out10.0700 XPM109 B
AeLjYwoN…qGBxBQFd
5640ab3bbb77ad…840255386e2ee6
4 in β†’ 2 out1000.0100 XPM669 B
Ac1cfJwa…9KirBzRBAS7iAF19…5ortYGqK
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.

1.578 Γ— 10⁹²(93-digit number)
15783156340250527576…19947189062209568000
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
1.578 Γ— 10⁹²(93-digit number)
15783156340250527576…19947189062209568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.156 Γ— 10⁹²(93-digit number)
31566312680501055153…39894378124419136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.313 Γ— 10⁹²(93-digit number)
63132625361002110307…79788756248838272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.262 Γ— 10⁹³(94-digit number)
12626525072200422061…59577512497676544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.525 Γ— 10⁹³(94-digit number)
25253050144400844122…19155024995353088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.050 Γ— 10⁹³(94-digit number)
50506100288801688245…38310049990706176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.010 Γ— 10⁹⁴(95-digit number)
10101220057760337649…76620099981412352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.020 Γ— 10⁹⁴(95-digit number)
20202440115520675298…53240199962824704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.040 Γ— 10⁹⁴(95-digit number)
40404880231041350596…06480399925649408001
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 264957

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 cb7cbea2a3028e97124d16c8e2b42839bd965a30ab8a101e0557a9bc97ce782e

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 #264,957 on Chainz β†—
Circulating Supply:57,647,441 XPMΒ·at block #6,800,421 Β· updates every 60s
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