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Home/Chain Registry/Block #1,390,043

Block #1,390,043

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/29/2015, 11:11:54 AM Β· Difficulty 10.8090 Β· 5,436,969 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c97d86ed16ee66ac9e3a68770543364d780b170c3c4a2a9012e90abfe30811af
View on Chainz β†—

Difficulty

10.809001

Transactions

1

Size

199 B

Version

2

Bits

0acf1aaf

Nonce

1,185,270,006

Timestamp

12/29/2015, 11:11:54 AM

Confirmations

5,436,969

Merkle Root

883bd2d5c095bd3840b1fc7a2e9f94eed3bd568453df538c3d62a10183040ef1
Transactions (1)
Coinbase883bd2d5c095bd…62a10183040ef1
1 in β†’ 1 out8.5500 XPM109 B
Af5dH6AN…Zn33dhya
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.

4.865 Γ— 10⁹⁴(95-digit number)
48659994758566384676…09946803438007747160
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
4.865 Γ— 10⁹⁴(95-digit number)
48659994758566384676…09946803438007747161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.731 Γ— 10⁹⁴(95-digit number)
97319989517132769353…19893606876015494321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.946 Γ— 10⁹⁡(96-digit number)
19463997903426553870…39787213752030988641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.892 Γ— 10⁹⁡(96-digit number)
38927995806853107741…79574427504061977281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.785 Γ— 10⁹⁡(96-digit number)
77855991613706215482…59148855008123954561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.557 Γ— 10⁹⁢(97-digit number)
15571198322741243096…18297710016247909121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.114 Γ— 10⁹⁢(97-digit number)
31142396645482486193…36595420032495818241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.228 Γ— 10⁹⁢(97-digit number)
62284793290964972386…73190840064991636481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.245 Γ— 10⁹⁷(98-digit number)
12456958658192994477…46381680129983272961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.491 Γ— 10⁹⁷(98-digit number)
24913917316385988954…92763360259966545921
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 1390043

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 c97d86ed16ee66ac9e3a68770543364d780b170c3c4a2a9012e90abfe30811af

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 #1,390,043 on Chainz β†—
Circulating Supply:57,860,273 XPMΒ·at block #6,827,011 Β· updates every 60s
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