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Block #3,003,525

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2019, 12:19:13 PM Β· Difficulty 11.2055 Β· 3,837,536 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
736eb08cb97848f200016e7ae2dcf16450c85660bece673ca70188bf9fd86349
View on Chainz β†—

Difficulty

11.205471

Transactions

1

Size

200 B

Version

2

Bits

0b3499c3

Nonce

498,786,810

Timestamp

1/10/2019, 12:19:13 PM

Confirmations

3,837,536

Merkle Root

650be36511a947b8ca38e8dacc5ab2673104bab476ea99e0e691812cba04f0d9
Transactions (1)
Coinbase650be36511a947…91812cba04f0d9
1 in β†’ 1 out7.9500 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.939 Γ— 10⁹⁴(95-digit number)
29397541470497780439…70652515091975745360
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.939 Γ— 10⁹⁴(95-digit number)
29397541470497780439…70652515091975745361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.879 Γ— 10⁹⁴(95-digit number)
58795082940995560879…41305030183951490721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.175 Γ— 10⁹⁡(96-digit number)
11759016588199112175…82610060367902981441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.351 Γ— 10⁹⁡(96-digit number)
23518033176398224351…65220120735805962881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.703 Γ— 10⁹⁡(96-digit number)
47036066352796448703…30440241471611925761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.407 Γ— 10⁹⁡(96-digit number)
94072132705592897406…60880482943223851521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.881 Γ— 10⁹⁢(97-digit number)
18814426541118579481…21760965886447703041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.762 Γ— 10⁹⁢(97-digit number)
37628853082237158962…43521931772895406081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.525 Γ— 10⁹⁢(97-digit number)
75257706164474317925…87043863545790812161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.505 Γ— 10⁹⁷(98-digit number)
15051541232894863585…74087727091581624321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.010 Γ— 10⁹⁷(98-digit number)
30103082465789727170…48175454183163248641
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3003525

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 736eb08cb97848f200016e7ae2dcf16450c85660bece673ca70188bf9fd86349

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 #3,003,525 on Chainz β†—
Circulating Supply:57,972,851 XPMΒ·at block #6,841,060 Β· updates every 60s
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