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Home/Chain Registry/Block #3,008,057

Block #3,008,057

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2019, 4:03:18 PM Β· Difficulty 11.2038 Β· 3,835,678 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
61f2eff660e9b551ee98e43e8de9f4aee8a61984f13b3501ff98cbed99cdc4b2
View on Chainz β†—

Difficulty

11.203779

Transactions

1

Size

200 B

Version

2

Bits

0b342ad5

Nonce

1,273,827,246

Timestamp

1/13/2019, 4:03:18 PM

Confirmations

3,835,678

Merkle Root

731c0f8625a84a6c6f1ea3552316cfd850c8c4e2c0a6a8e2e5b7559fe1851be5
Transactions (1)
Coinbase731c0f8625a84a…b7559fe1851be5
1 in β†’ 1 out7.9500 XPM109 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.

3.197 Γ— 10⁹⁢(97-digit number)
31970755931805914683…17796837170719641600
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
3.197 Γ— 10⁹⁢(97-digit number)
31970755931805914683…17796837170719641599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.394 Γ— 10⁹⁢(97-digit number)
63941511863611829367…35593674341439283199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.278 Γ— 10⁹⁷(98-digit number)
12788302372722365873…71187348682878566399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.557 Γ— 10⁹⁷(98-digit number)
25576604745444731747…42374697365757132799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.115 Γ— 10⁹⁷(98-digit number)
51153209490889463494…84749394731514265599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.023 Γ— 10⁹⁸(99-digit number)
10230641898177892698…69498789463028531199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.046 Γ— 10⁹⁸(99-digit number)
20461283796355785397…38997578926057062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.092 Γ— 10⁹⁸(99-digit number)
40922567592711570795…77995157852114124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.184 Γ— 10⁹⁸(99-digit number)
81845135185423141590…55990315704228249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.636 Γ— 10⁹⁹(100-digit number)
16369027037084628318…11980631408456499199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.273 Γ— 10⁹⁹(100-digit number)
32738054074169256636…23961262816912998399
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 3008057

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 61f2eff660e9b551ee98e43e8de9f4aee8a61984f13b3501ff98cbed99cdc4b2

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 #3,008,057 on Chainz β†—
Circulating Supply:57,994,248 XPMΒ·at block #6,843,734 Β· updates every 60s
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