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Home/Chain Registry/Block #3,003,951

Block #3,003,951

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2019, 7:10:37 PM Β· Difficulty 11.2078 Β· 3,838,443 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57abeff2a0a5babe67d6b897ca4ddb00817c0bfee571d2ac36ba60b3f3b4712e
View on Chainz β†—

Difficulty

11.207763

Transactions

1

Size

200 B

Version

2

Bits

0b352ff6

Nonce

544,167,112

Timestamp

1/10/2019, 7:10:37 PM

Confirmations

3,838,443

Merkle Root

c14965bc0a6f13bbde15eab6363a1e002199142d11dba74c5ca12075fd84760f
Transactions (1)
Coinbasec14965bc0a6f13…a12075fd84760f
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.

9.019 Γ— 10⁹⁡(96-digit number)
90198373940548735748…72439125186642556800
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
9.019 Γ— 10⁹⁡(96-digit number)
90198373940548735748…72439125186642556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.803 Γ— 10⁹⁢(97-digit number)
18039674788109747149…44878250373285113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.607 Γ— 10⁹⁢(97-digit number)
36079349576219494299…89756500746570227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.215 Γ— 10⁹⁢(97-digit number)
72158699152438988598…79513001493140454401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.443 Γ— 10⁹⁷(98-digit number)
14431739830487797719…59026002986280908801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.886 Γ— 10⁹⁷(98-digit number)
28863479660975595439…18052005972561817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.772 Γ— 10⁹⁷(98-digit number)
57726959321951190879…36104011945123635201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.154 Γ— 10⁹⁸(99-digit number)
11545391864390238175…72208023890247270401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.309 Γ— 10⁹⁸(99-digit number)
23090783728780476351…44416047780494540801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.618 Γ— 10⁹⁸(99-digit number)
46181567457560952703…88832095560989081601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.236 Γ— 10⁹⁸(99-digit number)
92363134915121905406…77664191121978163201
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 3003951

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 57abeff2a0a5babe67d6b897ca4ddb00817c0bfee571d2ac36ba60b3f3b4712e

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 #3,003,951 on Chainz β†—
Circulating Supply:57,983,563 XPMΒ·at block #6,842,393 Β· updates every 60s
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