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Home/Chain Registry/Block #1,346,393

Block #1,346,393

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2015, 9:00:13 PM Β· Difficulty 10.8219 Β· 5,448,424 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4240a51c56e02bee7f8c63c8795d351e5701bbf292cf21161c97efd4ec75f84e
View on Chainz β†—

Difficulty

10.821889

Transactions

1

Size

201 B

Version

2

Bits

0ad26752

Nonce

1,916,372,705

Timestamp

11/28/2015, 9:00:13 PM

Confirmations

5,448,424

Merkle Root

96c10d216b7edc1d4470442cf293640ec96fc5aa5b28e4369169768b06f41fe5
Transactions (1)
Coinbase96c10d216b7edc…69768b06f41fe5
1 in β†’ 1 out8.5300 XPM110 B
AWsmHzTm…TbLe3GSZ
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.

6.023 Γ— 10⁹⁢(97-digit number)
60232872383343137805…18977298551435776000
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
6.023 Γ— 10⁹⁢(97-digit number)
60232872383343137805…18977298551435776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.204 Γ— 10⁹⁷(98-digit number)
12046574476668627561…37954597102871552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.409 Γ— 10⁹⁷(98-digit number)
24093148953337255122…75909194205743104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.818 Γ— 10⁹⁷(98-digit number)
48186297906674510244…51818388411486208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.637 Γ— 10⁹⁷(98-digit number)
96372595813349020488…03636776822972416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.927 Γ— 10⁹⁸(99-digit number)
19274519162669804097…07273553645944832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.854 Γ— 10⁹⁸(99-digit number)
38549038325339608195…14547107291889664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.709 Γ— 10⁹⁸(99-digit number)
77098076650679216390…29094214583779328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.541 Γ— 10⁹⁹(100-digit number)
15419615330135843278…58188429167558656001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.083 Γ— 10⁹⁹(100-digit number)
30839230660271686556…16376858335117312001
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 1346393

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 4240a51c56e02bee7f8c63c8795d351e5701bbf292cf21161c97efd4ec75f84e

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 #1,346,393 on Chainz β†—
Circulating Supply:57,602,583 XPMΒ·at block #6,794,816 Β· updates every 60s
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