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Home/Chain Registry/Block #2,997,853

Block #2,997,853

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/6/2019, 9:16:25 AM Β· Difficulty 11.2468 Β· 3,844,985 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f1c805e211feebed04ebd04515e10d2f4a31cabe2deaf1ebbab611f93ba202d7
View on Chainz β†—

Difficulty

11.246822

Transactions

1

Size

200 B

Version

2

Bits

0b3f2fc2

Nonce

585,957,874

Timestamp

1/6/2019, 9:16:25 AM

Confirmations

3,844,985

Merkle Root

17c583d05dab739d93b2b64725209d3b1c661c3bb6b164d4e636a650b9079671
Transactions (1)
Coinbase17c583d05dab73…36a650b9079671
1 in β†’ 1 out7.8900 XPM110 B
AUhjokok…k5m93PZR
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.

1.071 Γ— 10⁹⁡(96-digit number)
10711473523915076507…40832561935720136960
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
1.071 Γ— 10⁹⁡(96-digit number)
10711473523915076507…40832561935720136959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.142 Γ— 10⁹⁡(96-digit number)
21422947047830153014…81665123871440273919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.284 Γ— 10⁹⁡(96-digit number)
42845894095660306029…63330247742880547839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.569 Γ— 10⁹⁡(96-digit number)
85691788191320612059…26660495485761095679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.713 Γ— 10⁹⁢(97-digit number)
17138357638264122411…53320990971522191359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.427 Γ— 10⁹⁢(97-digit number)
34276715276528244823…06641981943044382719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.855 Γ— 10⁹⁢(97-digit number)
68553430553056489647…13283963886088765439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁷(98-digit number)
13710686110611297929…26567927772177530879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁷(98-digit number)
27421372221222595859…53135855544355061759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.484 Γ— 10⁹⁷(98-digit number)
54842744442445191718…06271711088710123519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.096 Γ— 10⁹⁸(99-digit number)
10968548888489038343…12543422177420247039
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 2997853

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 f1c805e211feebed04ebd04515e10d2f4a31cabe2deaf1ebbab611f93ba202d7

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 #2,997,853 on Chainz β†—
Circulating Supply:57,987,047 XPMΒ·at block #6,842,837 Β· updates every 60s
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