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Block #2,679,345

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2018, 10:46:37 PM Β· Difficulty 11.6936 Β· 4,159,903 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed859e7f14dea8bd11589e048018e7f26eee6ff335d64ad1a592dee5a636e9ca
View on Chainz β†—

Difficulty

11.693583

Transactions

1

Size

200 B

Version

2

Bits

0bb18eaa

Nonce

947,349,498

Timestamp

5/26/2018, 10:46:37 PM

Confirmations

4,159,903

Merkle Root

012d9cd36df06192ea16a78a7d676bf752d753de65e93fcfbe0f65e63a5a810d
Transactions (1)
Coinbase012d9cd36df061…0f65e63a5a810d
1 in β†’ 1 out7.3000 XPM110 B
AZawbvkB…9Vfv33KT
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.

1.243 Γ— 10⁹⁴(95-digit number)
12437276331795884002…67628705995212938800
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
1.243 Γ— 10⁹⁴(95-digit number)
12437276331795884002…67628705995212938801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.487 Γ— 10⁹⁴(95-digit number)
24874552663591768005…35257411990425877601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.974 Γ— 10⁹⁴(95-digit number)
49749105327183536011…70514823980851755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.949 Γ— 10⁹⁴(95-digit number)
99498210654367072023…41029647961703510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.989 Γ— 10⁹⁡(96-digit number)
19899642130873414404…82059295923407020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.979 Γ— 10⁹⁡(96-digit number)
39799284261746828809…64118591846814041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.959 Γ— 10⁹⁡(96-digit number)
79598568523493657619…28237183693628083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.591 Γ— 10⁹⁢(97-digit number)
15919713704698731523…56474367387256166401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.183 Γ— 10⁹⁢(97-digit number)
31839427409397463047…12948734774512332801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.367 Γ— 10⁹⁢(97-digit number)
63678854818794926095…25897469549024665601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.273 Γ— 10⁹⁷(98-digit number)
12735770963758985219…51794939098049331201
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 2679345

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 ed859e7f14dea8bd11589e048018e7f26eee6ff335d64ad1a592dee5a636e9ca

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 #2,679,345 on Chainz β†—
Circulating Supply:57,958,266 XPMΒ·at block #6,839,247 Β· updates every 60s
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