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Block #1,424,683

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/23/2016, 3:05:13 AM Β· Difficulty 10.7742 Β· 5,419,730 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8a005d41a5933c9189fd48294785fa025e4054be8abb9f0f2f7e45c2b629f322
View on Chainz β†—

Difficulty

10.774170

Transactions

1

Size

200 B

Version

2

Bits

0ac63004

Nonce

1,023,226,553

Timestamp

1/23/2016, 3:05:13 AM

Confirmations

5,419,730

Merkle Root

515e43e4d4c4973ea891e6a98df328f4152c4c8dd1600ad39e784b6ba8c4a0b5
Transactions (1)
Coinbase515e43e4d4c497…784b6ba8c4a0b5
1 in β†’ 1 out8.6000 XPM110 B
AQrXPYA1…yqXFb2bo
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.

1.529 Γ— 10⁹⁡(96-digit number)
15291594617248822964…90715893755449394720
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
1.529 Γ— 10⁹⁡(96-digit number)
15291594617248822964…90715893755449394721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.058 Γ— 10⁹⁡(96-digit number)
30583189234497645928…81431787510898789441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.116 Γ— 10⁹⁡(96-digit number)
61166378468995291856…62863575021797578881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.223 Γ— 10⁹⁢(97-digit number)
12233275693799058371…25727150043595157761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.446 Γ— 10⁹⁢(97-digit number)
24466551387598116742…51454300087190315521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.893 Γ— 10⁹⁢(97-digit number)
48933102775196233485…02908600174380631041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.786 Γ— 10⁹⁢(97-digit number)
97866205550392466970…05817200348761262081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.957 Γ— 10⁹⁷(98-digit number)
19573241110078493394…11634400697522524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.914 Γ— 10⁹⁷(98-digit number)
39146482220156986788…23268801395045048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.829 Γ— 10⁹⁷(98-digit number)
78292964440313973576…46537602790090096641
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 1424683

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 8a005d41a5933c9189fd48294785fa025e4054be8abb9f0f2f7e45c2b629f322

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 #1,424,683 on Chainz β†—
Circulating Supply:57,999,698 XPMΒ·at block #6,844,412 Β· updates every 60s
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