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Home/Chain Registry/Block #2,950,498

Block #2,950,498

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2018, 5:09:44 PM Β· Difficulty 11.3968 Β· 3,887,496 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2729fa1a89b04ab887d0eb05cdd613eb936be55772e4e703b8037e12d5d9282d
View on Chainz β†—

Difficulty

11.396811

Transactions

1

Size

201 B

Version

2

Bits

0b65956e

Nonce

1,491,949,631

Timestamp

12/3/2018, 5:09:44 PM

Confirmations

3,887,496

Merkle Root

96a8732fc714e6d76863cd75e229e2fd7007938f0a6ccaa6d3efb8747193f47d
Transactions (1)
Coinbase96a8732fc714e6…efb8747193f47d
1 in β†’ 1 out7.6900 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.

8.443 Γ— 10⁹⁡(96-digit number)
84434428121120044374…92205492226409646080
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
8.443 Γ— 10⁹⁡(96-digit number)
84434428121120044374…92205492226409646081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.688 Γ— 10⁹⁢(97-digit number)
16886885624224008874…84410984452819292161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.377 Γ— 10⁹⁢(97-digit number)
33773771248448017749…68821968905638584321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.754 Γ— 10⁹⁢(97-digit number)
67547542496896035499…37643937811277168641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.350 Γ— 10⁹⁷(98-digit number)
13509508499379207099…75287875622554337281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.701 Γ— 10⁹⁷(98-digit number)
27019016998758414199…50575751245108674561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.403 Γ— 10⁹⁷(98-digit number)
54038033997516828399…01151502490217349121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.080 Γ— 10⁹⁸(99-digit number)
10807606799503365679…02303004980434698241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.161 Γ— 10⁹⁸(99-digit number)
21615213599006731359…04606009960869396481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.323 Γ— 10⁹⁸(99-digit number)
43230427198013462719…09212019921738792961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.646 Γ— 10⁹⁸(99-digit number)
86460854396026925439…18424039843477585921
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 2950498

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 2729fa1a89b04ab887d0eb05cdd613eb936be55772e4e703b8037e12d5d9282d

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 #2,950,498 on Chainz β†—
Circulating Supply:57,948,305 XPMΒ·at block #6,837,993 Β· updates every 60s
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