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Home/Chain Registry/Block #3,008,426

Block #3,008,426

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2019, 10:23:28 PM Β· Difficulty 11.2024 Β· 3,834,502 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5602c4039d7a8ef7f63692b2f5ec1ccad2d52b0f3540bc889d8c72e3a09b7c38
View on Chainz β†—

Difficulty

11.202377

Transactions

2

Size

1.72 KB

Version

2

Bits

0b33cefc

Nonce

107,729,016

Timestamp

1/13/2019, 10:23:28 PM

Confirmations

3,834,502

Merkle Root

d01f7eddb127a75f92416c147706824cc3b39642c762d1867b707e1ceb01d1af
Transactions (2)
Coinbase14dac96db45cb9…37cacd89abeb5f
1 in β†’ 1 out7.9800 XPM110 B
AUhjokok…k5m93PZR
7231ebf5597923…b98ab0185e5cdf
10 in β†’ 2 out505.3726 XPM1.52 KB
AbadyHGq…syxq2CpkAeKLDKpW…3J3T8WsL
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.

1.359 Γ— 10⁹⁡(96-digit number)
13599630102750054197…46918705576865319040
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
1.359 Γ— 10⁹⁡(96-digit number)
13599630102750054197…46918705576865319039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.719 Γ— 10⁹⁡(96-digit number)
27199260205500108394…93837411153730638079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.439 Γ— 10⁹⁡(96-digit number)
54398520411000216789…87674822307461276159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.087 Γ— 10⁹⁢(97-digit number)
10879704082200043357…75349644614922552319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.175 Γ— 10⁹⁢(97-digit number)
21759408164400086715…50699289229845104639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.351 Γ— 10⁹⁢(97-digit number)
43518816328800173431…01398578459690209279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.703 Γ— 10⁹⁢(97-digit number)
87037632657600346863…02797156919380418559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.740 Γ— 10⁹⁷(98-digit number)
17407526531520069372…05594313838760837119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.481 Γ— 10⁹⁷(98-digit number)
34815053063040138745…11188627677521674239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.963 Γ— 10⁹⁷(98-digit number)
69630106126080277490…22377255355043348479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁸(99-digit number)
13926021225216055498…44754510710086696959
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 3008426

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 5602c4039d7a8ef7f63692b2f5ec1ccad2d52b0f3540bc889d8c72e3a09b7c38

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 #3,008,426 on Chainz β†—
Circulating Supply:57,987,772 XPMΒ·at block #6,842,927 Β· updates every 60s
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