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Block #1,310,722

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/3/2015, 12:14:03 PM Β· Difficulty 10.8485 Β· 5,515,843 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0fc750df9a4e8ae17987e008047457ce69febc38cf16fd626595f1c5ffd1bba6
View on Chainz β†—

Difficulty

10.848521

Transactions

1

Size

200 B

Version

2

Bits

0ad938a5

Nonce

601,210,531

Timestamp

11/3/2015, 12:14:03 PM

Confirmations

5,515,843

Merkle Root

660fd9b6608b685209569d2f4b0a99a857e8de5b558c869e772b0b050449bf90
Transactions (1)
Coinbase660fd9b6608b68…2b0b050449bf90
1 in β†’ 1 out8.4800 XPM109 B
ARrb5J1F…XULH6iYt
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.

1.007 Γ— 10⁹⁷(98-digit number)
10076259170426966509…47696004323536527360
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
1.007 Γ— 10⁹⁷(98-digit number)
10076259170426966509…47696004323536527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.015 Γ— 10⁹⁷(98-digit number)
20152518340853933019…95392008647073054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.030 Γ— 10⁹⁷(98-digit number)
40305036681707866039…90784017294146109441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.061 Γ— 10⁹⁷(98-digit number)
80610073363415732079…81568034588292218881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.612 Γ— 10⁹⁸(99-digit number)
16122014672683146415…63136069176584437761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.224 Γ— 10⁹⁸(99-digit number)
32244029345366292831…26272138353168875521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.448 Γ— 10⁹⁸(99-digit number)
64488058690732585663…52544276706337751041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.289 Γ— 10⁹⁹(100-digit number)
12897611738146517132…05088553412675502081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.579 Γ— 10⁹⁹(100-digit number)
25795223476293034265…10177106825351004161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.159 Γ— 10⁹⁹(100-digit number)
51590446952586068530…20354213650702008321
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 1310722

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 0fc750df9a4e8ae17987e008047457ce69febc38cf16fd626595f1c5ffd1bba6

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 #1,310,722 on Chainz β†—
Circulating Supply:57,856,672 XPMΒ·at block #6,826,564 Β· updates every 60s
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