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Block #2,950,499

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/3/2018, 5:10:33 PM Β· Difficulty 11.3966 Β· 3,887,867 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e33e56bb112fb753e98bcfa17581785b2835b849ae976fad802134334c55f84a
View on Chainz β†—

Difficulty

11.396614

Transactions

1

Size

200 B

Version

2

Bits

0b65887e

Nonce

1,319,432,036

Timestamp

12/3/2018, 5:10:33 PM

Confirmations

3,887,867

Merkle Root

6eae58010c001890511b1aa573f8e102a26536bca19d332fd1c9a697f0f7f6ac
Transactions (1)
Coinbase6eae58010c0018…c9a697f0f7f6ac
1 in β†’ 1 out7.6900 XPM109 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.

6.024 Γ— 10⁹⁢(97-digit number)
60246351957820935841…10179733588754793600
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
6.024 Γ— 10⁹⁢(97-digit number)
60246351957820935841…10179733588754793601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.204 Γ— 10⁹⁷(98-digit number)
12049270391564187168…20359467177509587201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.409 Γ— 10⁹⁷(98-digit number)
24098540783128374336…40718934355019174401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.819 Γ— 10⁹⁷(98-digit number)
48197081566256748673…81437868710038348801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.639 Γ— 10⁹⁷(98-digit number)
96394163132513497346…62875737420076697601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.927 Γ— 10⁹⁸(99-digit number)
19278832626502699469…25751474840153395201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.855 Γ— 10⁹⁸(99-digit number)
38557665253005398938…51502949680306790401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.711 Γ— 10⁹⁸(99-digit number)
77115330506010797877…03005899360613580801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.542 Γ— 10⁹⁹(100-digit number)
15423066101202159575…06011798721227161601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.084 Γ— 10⁹⁹(100-digit number)
30846132202404319150…12023597442454323201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.169 Γ— 10⁹⁹(100-digit number)
61692264404808638301…24047194884908646401
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 2950499

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 e33e56bb112fb753e98bcfa17581785b2835b849ae976fad802134334c55f84a

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 #2,950,499 on Chainz β†—
Circulating Supply:57,951,196 XPMΒ·at block #6,838,365 Β· updates every 60s
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