XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,346,390

Block #1,346,390

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2015, 8:56:14 PM Β· Difficulty 10.8220 Β· 5,454,433 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
813397d2ecb9dba0975de87c6b9e4cf0a5dbf6aee3f2ff4a4955471e3551bae7
View on Chainz β†—

Difficulty

10.821987

Transactions

1

Size

199 B

Version

2

Bits

0ad26db8

Nonce

39,675,069

Timestamp

11/28/2015, 8:56:14 PM

Confirmations

5,454,433

Merkle Root

43d66db4334d21ef84a41d517a4ceca7e1042083b240576eab650bbf4054039c
Transactions (1)
Coinbase43d66db4334d21…650bbf4054039c
1 in β†’ 1 out8.5300 XPM109 B
Aayr9SWM…NdeqoYcY
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.

6.609 Γ— 10⁹⁴(95-digit number)
66094939193167761236…21469588501492127520
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
6.609 Γ— 10⁹⁴(95-digit number)
66094939193167761236…21469588501492127521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.321 Γ— 10⁹⁡(96-digit number)
13218987838633552247…42939177002984255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.643 Γ— 10⁹⁡(96-digit number)
26437975677267104494…85878354005968510081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.287 Γ— 10⁹⁡(96-digit number)
52875951354534208989…71756708011937020161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.057 Γ— 10⁹⁢(97-digit number)
10575190270906841797…43513416023874040321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.115 Γ— 10⁹⁢(97-digit number)
21150380541813683595…87026832047748080641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.230 Γ— 10⁹⁢(97-digit number)
42300761083627367191…74053664095496161281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.460 Γ— 10⁹⁢(97-digit number)
84601522167254734382…48107328190992322561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.692 Γ— 10⁹⁷(98-digit number)
16920304433450946876…96214656381984645121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.384 Γ— 10⁹⁷(98-digit number)
33840608866901893753…92429312763969290241
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 1346390

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 813397d2ecb9dba0975de87c6b9e4cf0a5dbf6aee3f2ff4a4955471e3551bae7

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 #1,346,390 on Chainz β†—
Circulating Supply:57,650,640 XPMΒ·at block #6,800,822 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK