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Home/Chain Registry/Block #2,946,167

Block #2,946,167

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2018, 4:55:46 PM Β· Difficulty 11.3967 Β· 3,892,278 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ad8068c15c04a39ad474ff6b5ed3c6468e43043fecf70a0cf45ec1a4f23330a
View on Chainz β†—

Difficulty

11.396739

Transactions

2

Size

392 B

Version

2

Bits

0b6590ae

Nonce

199,903,906

Timestamp

11/30/2018, 4:55:46 PM

Confirmations

3,892,278

Merkle Root

d59d5c5b053ad7bd92bc6195b741a6862db4f893a442e557419cd07054fee6f9
Transactions (2)
Coinbase06305ef565df00…0340b3280a9351
1 in β†’ 1 out7.7000 XPM110 B
AUMQRepm…tAfKmdW1
6c329f8489f494…405ffa3b9e3562
1 in β†’ 2 out7.6800 XPM192 B
AUhjokok…k5m93PZRAWaYC9BA…1BzTFe5J
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.

2.978 Γ— 10⁹⁡(96-digit number)
29783213353236937558…15719751334064583040
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
2.978 Γ— 10⁹⁡(96-digit number)
29783213353236937558…15719751334064583041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.956 Γ— 10⁹⁡(96-digit number)
59566426706473875117…31439502668129166081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.191 Γ— 10⁹⁢(97-digit number)
11913285341294775023…62879005336258332161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.382 Γ— 10⁹⁢(97-digit number)
23826570682589550046…25758010672516664321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.765 Γ— 10⁹⁢(97-digit number)
47653141365179100093…51516021345033328641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.530 Γ— 10⁹⁢(97-digit number)
95306282730358200187…03032042690066657281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.906 Γ— 10⁹⁷(98-digit number)
19061256546071640037…06064085380133314561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.812 Γ— 10⁹⁷(98-digit number)
38122513092143280074…12128170760266629121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.624 Γ— 10⁹⁷(98-digit number)
76245026184286560149…24256341520533258241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.524 Γ— 10⁹⁸(99-digit number)
15249005236857312029…48512683041066516481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.049 Γ— 10⁹⁸(99-digit number)
30498010473714624059…97025366082133032961
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 2946167

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 6ad8068c15c04a39ad474ff6b5ed3c6468e43043fecf70a0cf45ec1a4f23330a

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 #2,946,167 on Chainz β†—
Circulating Supply:57,951,838 XPMΒ·at block #6,838,444 Β· updates every 60s
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