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Home/Chain Registry/Block #3,054,182

Block #3,054,182

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/15/2019, 4:59:26 PM Β· Difficulty 11.0028 Β· 3,785,087 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4294ee05aea026ab9bd4f0922b7b35a1a4f41a144a39e91ccba07912746c1a79
View on Chainz β†—

Difficulty

11.002850

Transactions

1

Size

200 B

Version

2

Bits

0b00bac6

Nonce

177,476,701

Timestamp

2/15/2019, 4:59:26 PM

Confirmations

3,785,087

Merkle Root

3d0bd00e39c5155aa60787eb349130568138c6d613fbc390bfcc85ec19b51af7
Transactions (1)
Coinbase3d0bd00e39c515…cc85ec19b51af7
1 in β†’ 1 out8.2500 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.

7.635 Γ— 10⁹⁢(97-digit number)
76351964465038505481…80255107901339392000
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
7.635 Γ— 10⁹⁢(97-digit number)
76351964465038505481…80255107901339392001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.527 Γ— 10⁹⁷(98-digit number)
15270392893007701096…60510215802678784001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.054 Γ— 10⁹⁷(98-digit number)
30540785786015402192…21020431605357568001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.108 Γ— 10⁹⁷(98-digit number)
61081571572030804385…42040863210715136001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.221 Γ— 10⁹⁸(99-digit number)
12216314314406160877…84081726421430272001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.443 Γ— 10⁹⁸(99-digit number)
24432628628812321754…68163452842860544001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.886 Γ— 10⁹⁸(99-digit number)
48865257257624643508…36326905685721088001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.773 Γ— 10⁹⁸(99-digit number)
97730514515249287016…72653811371442176001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.954 Γ— 10⁹⁹(100-digit number)
19546102903049857403…45307622742884352001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.909 Γ— 10⁹⁹(100-digit number)
39092205806099714806…90615245485768704001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.818 Γ— 10⁹⁹(100-digit number)
78184411612199429613…81230490971537408001
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 3054182

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 4294ee05aea026ab9bd4f0922b7b35a1a4f41a144a39e91ccba07912746c1a79

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 #3,054,182 on Chainz β†—
Circulating Supply:57,958,436 XPMΒ·at block #6,839,268 Β· updates every 60s
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