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Home/Chain Registry/Block #2,150,285

Block #2,150,285

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/7/2017, 3:04:25 PM Β· Difficulty 10.8990 Β· 4,692,601 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
03d974a4487a59df4cf7500605bee15957ef9d7091dfdb177d970cd8d85c9a7e
View on Chainz β†—

Difficulty

10.899019

Transactions

1

Size

199 B

Version

2

Bits

0ae6261d

Nonce

451,410,867

Timestamp

6/7/2017, 3:04:25 PM

Confirmations

4,692,601

Merkle Root

fe1c5e329ebca7a715eaef77b09a8408d5c347b760e86ef2d7002862422917d0
Transactions (1)
Coinbasefe1c5e329ebca7…002862422917d0
1 in β†’ 1 out8.4000 XPM109 B
ALY4PGi2…NZtg7G3E
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.

5.074 Γ— 10⁹⁡(96-digit number)
50747520281291047200…18546940239608664640
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
5.074 Γ— 10⁹⁡(96-digit number)
50747520281291047200…18546940239608664639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.014 Γ— 10⁹⁢(97-digit number)
10149504056258209440…37093880479217329279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.029 Γ— 10⁹⁢(97-digit number)
20299008112516418880…74187760958434658559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.059 Γ— 10⁹⁢(97-digit number)
40598016225032837760…48375521916869317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.119 Γ— 10⁹⁢(97-digit number)
81196032450065675520…96751043833738634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.623 Γ— 10⁹⁷(98-digit number)
16239206490013135104…93502087667477268479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.247 Γ— 10⁹⁷(98-digit number)
32478412980026270208…87004175334954536959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.495 Γ— 10⁹⁷(98-digit number)
64956825960052540416…74008350669909073919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.299 Γ— 10⁹⁸(99-digit number)
12991365192010508083…48016701339818147839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.598 Γ— 10⁹⁸(99-digit number)
25982730384021016166…96033402679636295679
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2150285

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 03d974a4487a59df4cf7500605bee15957ef9d7091dfdb177d970cd8d85c9a7e

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 #2,150,285 on Chainz β†—
Circulating Supply:57,987,434 XPMΒ·at block #6,842,885 Β· updates every 60s
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