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Block #265,260

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2013, 9:51:50 AM Β· Difficulty 9.9630 Β· 6,529,599 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4985bcfa439ab49bf17d1fa8bcbea978d8fe3553f94c705beb932008cdb912c8
View on Chainz β†—

Height

#265,260

Difficulty

9.962998

Transactions

1

Size

206 B

Version

2

Bits

09f6870a

Nonce

16,784,841

Timestamp

11/19/2013, 9:51:50 AM

Confirmations

6,529,599

Merkle Root

c9bd1ec64b27537179317d42a818a621ae4907f535e902a20dd9c5b8009b5b57
Transactions (1)
Coinbasec9bd1ec64b2753…d9c5b8009b5b57
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.

2.200 Γ— 10⁹⁴(95-digit number)
22007289540775696253…34647534162477136580
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
2.200 Γ— 10⁹⁴(95-digit number)
22007289540775696253…34647534162477136581
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.401 Γ— 10⁹⁴(95-digit number)
44014579081551392506…69295068324954273161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.802 Γ— 10⁹⁴(95-digit number)
88029158163102785012…38590136649908546321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.760 Γ— 10⁹⁡(96-digit number)
17605831632620557002…77180273299817092641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.521 Γ— 10⁹⁡(96-digit number)
35211663265241114005…54360546599634185281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.042 Γ— 10⁹⁡(96-digit number)
70423326530482228010…08721093199268370561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.408 Γ— 10⁹⁢(97-digit number)
14084665306096445602…17442186398536741121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.816 Γ— 10⁹⁢(97-digit number)
28169330612192891204…34884372797073482241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.633 Γ— 10⁹⁢(97-digit number)
56338661224385782408…69768745594146964481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.126 Γ— 10⁹⁷(98-digit number)
11267732244877156481…39537491188293928961
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 265260

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 4985bcfa439ab49bf17d1fa8bcbea978d8fe3553f94c705beb932008cdb912c8

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 #265,260 on Chainz β†—
Circulating Supply:57,602,903 XPMΒ·at block #6,794,858 Β· updates every 60s
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