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Home/Chain Registry/Block #3,007,666

Block #3,007,666

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2019, 9:11:11 AM Β· Difficulty 11.2070 Β· 3,835,457 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ce244b7653b6b7d2f3a4aa5ad731564b2d5fca184a7a8648951e52656de48b7f
View on Chainz β†—

Difficulty

11.207045

Transactions

1

Size

200 B

Version

2

Bits

0b3500e9

Nonce

154,363,770

Timestamp

1/13/2019, 9:11:11 AM

Confirmations

3,835,457

Merkle Root

c624ab6baba4ed6344834d5fa8211cefa97ad3ee885528fd86a3cc32e02e448e
Transactions (1)
Coinbasec624ab6baba4ed…a3cc32e02e448e
1 in β†’ 1 out7.9500 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.

1.027 Γ— 10⁹⁡(96-digit number)
10273722775514359337…09730360131701498080
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
1.027 Γ— 10⁹⁡(96-digit number)
10273722775514359337…09730360131701498079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.054 Γ— 10⁹⁡(96-digit number)
20547445551028718675…19460720263402996159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.109 Γ— 10⁹⁡(96-digit number)
41094891102057437350…38921440526805992319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.218 Γ— 10⁹⁡(96-digit number)
82189782204114874701…77842881053611984639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.643 Γ— 10⁹⁢(97-digit number)
16437956440822974940…55685762107223969279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.287 Γ— 10⁹⁢(97-digit number)
32875912881645949880…11371524214447938559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.575 Γ— 10⁹⁢(97-digit number)
65751825763291899761…22743048428895877119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.315 Γ— 10⁹⁷(98-digit number)
13150365152658379952…45486096857791754239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.630 Γ— 10⁹⁷(98-digit number)
26300730305316759904…90972193715583508479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.260 Γ— 10⁹⁷(98-digit number)
52601460610633519808…81944387431167016959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.052 Γ— 10⁹⁸(99-digit number)
10520292122126703961…63888774862334033919
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 3007666

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 ce244b7653b6b7d2f3a4aa5ad731564b2d5fca184a7a8648951e52656de48b7f

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 #3,007,666 on Chainz β†—
Circulating Supply:57,989,350 XPMΒ·at block #6,843,122 Β· updates every 60s
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