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Home/Chain Registry/Block #3,373,847

Block #3,373,847

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/29/2019, 9:00:27 AM Β· Difficulty 10.9947 Β· 3,467,848 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3bd22db3ba1a6e96415f683e634873ef62811de33197fa47200bb0ddb7d78134
View on Chainz β†—

Difficulty

10.994714

Transactions

1

Size

201 B

Version

2

Bits

0afea590

Nonce

1,235,857,881

Timestamp

9/29/2019, 9:00:27 AM

Confirmations

3,467,848

Merkle Root

105e6ca7b55712b90d93417f799a58081f3c28050cddddb94080ab71f0d2ef7f
Transactions (1)
Coinbase105e6ca7b55712…80ab71f0d2ef7f
1 in β†’ 1 out8.2600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

2.179 Γ— 10⁹⁢(97-digit number)
21794298561312605288…59665503830325992000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.179 Γ— 10⁹⁢(97-digit number)
21794298561312605288…59665503830325991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.358 Γ— 10⁹⁢(97-digit number)
43588597122625210577…19331007660651983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.717 Γ— 10⁹⁢(97-digit number)
87177194245250421155…38662015321303967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.743 Γ— 10⁹⁷(98-digit number)
17435438849050084231…77324030642607935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.487 Γ— 10⁹⁷(98-digit number)
34870877698100168462…54648061285215871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.974 Γ— 10⁹⁷(98-digit number)
69741755396200336924…09296122570431743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.394 Γ— 10⁹⁸(99-digit number)
13948351079240067384…18592245140863487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.789 Γ— 10⁹⁸(99-digit number)
27896702158480134769…37184490281726975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.579 Γ— 10⁹⁸(99-digit number)
55793404316960269539…74368980563453951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.115 Γ— 10⁹⁹(100-digit number)
11158680863392053907…48737961126907903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.231 Γ— 10⁹⁹(100-digit number)
22317361726784107815…97475922253815807999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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
RareChain length 11
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 3373847

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 3bd22db3ba1a6e96415f683e634873ef62811de33197fa47200bb0ddb7d78134

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 #3,373,847 on Chainz β†—
Circulating Supply:57,977,938 XPMΒ·at block #6,841,694 Β· updates every 60s
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