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Home/Chain Registry/Block #2,997,462

Block #2,997,462

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/6/2019, 2:19:25 AM Β· Difficulty 11.2506 Β· 3,833,702 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9971f5c2feb062cf13e46d22df9ddc153a7dfaeb129c74d4783267df5e09b957
View on Chainz β†—

Difficulty

11.250624

Transactions

1

Size

201 B

Version

2

Bits

0b4028e0

Nonce

577,866,365

Timestamp

1/6/2019, 2:19:25 AM

Confirmations

3,833,702

Merkle Root

3134e7baad55860c10383278c68b950a1228d78d63ddd2ae331da184b547b73b
Transactions (1)
Coinbase3134e7baad5586…1da184b547b73b
1 in β†’ 1 out7.8900 XPM110 B
AbXwmGxD…4XXYP765
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.

4.288 Γ— 10⁹⁢(97-digit number)
42883718898666492144…14188341056783585280
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
4.288 Γ— 10⁹⁢(97-digit number)
42883718898666492144…14188341056783585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.576 Γ— 10⁹⁢(97-digit number)
85767437797332984289…28376682113567170559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.715 Γ— 10⁹⁷(98-digit number)
17153487559466596857…56753364227134341119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.430 Γ— 10⁹⁷(98-digit number)
34306975118933193715…13506728454268682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.861 Γ— 10⁹⁷(98-digit number)
68613950237866387431…27013456908537364479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.372 Γ— 10⁹⁸(99-digit number)
13722790047573277486…54026913817074728959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.744 Γ— 10⁹⁸(99-digit number)
27445580095146554972…08053827634149457919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.489 Γ— 10⁹⁸(99-digit number)
54891160190293109945…16107655268298915839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁹(100-digit number)
10978232038058621989…32215310536597831679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.195 Γ— 10⁹⁹(100-digit number)
21956464076117243978…64430621073195663359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.391 Γ— 10⁹⁹(100-digit number)
43912928152234487956…28861242146391326719
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 2997462

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 9971f5c2feb062cf13e46d22df9ddc153a7dfaeb129c74d4783267df5e09b957

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 #2,997,462 on Chainz β†—
Circulating Supply:57,893,453 XPMΒ·at block #6,831,163 Β· updates every 60s
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