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Home/Chain Registry/Block #3,016,797

Block #3,016,797

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/19/2019, 9:33:02 PM Β· Difficulty 11.1670 Β· 3,825,448 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
274a2b28028cbf2f5d2bcef57d2883e420c84b376b596e6ca1a8d31124f50336
View on Chainz β†—

Difficulty

11.166985

Transactions

1

Size

199 B

Version

2

Bits

0b2abf87

Nonce

579,550,322

Timestamp

1/19/2019, 9:33:02 PM

Confirmations

3,825,448

Merkle Root

f9bdea80e4203773f53c4fc73ee92c2fadb89d64f1a38ee60bf3895d04c5acaa
Transactions (1)
Coinbasef9bdea80e42037…f3895d04c5acaa
1 in β†’ 1 out8.0100 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.

2.408 Γ— 10⁹¹(92-digit number)
24085394899154212848…35619780335289943200
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
2.408 Γ— 10⁹¹(92-digit number)
24085394899154212848…35619780335289943201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.817 Γ— 10⁹¹(92-digit number)
48170789798308425696…71239560670579886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.634 Γ— 10⁹¹(92-digit number)
96341579596616851392…42479121341159772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.926 Γ— 10⁹²(93-digit number)
19268315919323370278…84958242682319545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.853 Γ— 10⁹²(93-digit number)
38536631838646740556…69916485364639091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.707 Γ— 10⁹²(93-digit number)
77073263677293481113…39832970729278182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.541 Γ— 10⁹³(94-digit number)
15414652735458696222…79665941458556364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.082 Γ— 10⁹³(94-digit number)
30829305470917392445…59331882917112729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.165 Γ— 10⁹³(94-digit number)
61658610941834784891…18663765834225459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.233 Γ— 10⁹⁴(95-digit number)
12331722188366956978…37327531668450918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.466 Γ— 10⁹⁴(95-digit number)
24663444376733913956…74655063336901836801
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 3016797

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 274a2b28028cbf2f5d2bcef57d2883e420c84b376b596e6ca1a8d31124f50336

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 #3,016,797 on Chainz β†—
Circulating Supply:57,982,358 XPMΒ·at block #6,842,244 Β· updates every 60s
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