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Block #1,268,260

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/5/2015, 3:32:04 PM Β· Difficulty 10.8173 Β· 5,557,962 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d62b66216e55ce105b071dc744de1257595c036cccac4c6729f07f6d5447842a
View on Chainz β†—

Difficulty

10.817326

Transactions

1

Size

243 B

Version

2

Bits

0ad13c47

Nonce

14,359,275

Timestamp

10/5/2015, 3:32:04 PM

Confirmations

5,557,962

Merkle Root

0170d5307a9c92983e10e63e08ac9fdbf94f6b1f1fd76f1602993249451a3606
Transactions (1)
Coinbase0170d5307a9c92…993249451a3606
1 in β†’ 2 out8.5300 XPM152 B
ATd5Bq5S…PcfPgHVjALPu3s2c…EJXLjVFh
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.

4.145 Γ— 10⁹⁢(97-digit number)
41453621993262563038…16570851789562247040
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
4.145 Γ— 10⁹⁢(97-digit number)
41453621993262563038…16570851789562247041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.290 Γ— 10⁹⁢(97-digit number)
82907243986525126076…33141703579124494081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.658 Γ— 10⁹⁷(98-digit number)
16581448797305025215…66283407158248988161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.316 Γ— 10⁹⁷(98-digit number)
33162897594610050430…32566814316497976321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.632 Γ— 10⁹⁷(98-digit number)
66325795189220100860…65133628632995952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.326 Γ— 10⁹⁸(99-digit number)
13265159037844020172…30267257265991905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.653 Γ— 10⁹⁸(99-digit number)
26530318075688040344…60534514531983810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.306 Γ— 10⁹⁸(99-digit number)
53060636151376080688…21069029063967621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.061 Γ— 10⁹⁹(100-digit number)
10612127230275216137…42138058127935242241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.122 Γ— 10⁹⁹(100-digit number)
21224254460550432275…84276116255870484481
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 1268260

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 d62b66216e55ce105b071dc744de1257595c036cccac4c6729f07f6d5447842a

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 #1,268,260 on Chainz β†—
Circulating Supply:57,853,909 XPMΒ·at block #6,826,221 Β· updates every 60s
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