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Home/Chain Registry/Block #2,679,141

Block #2,679,141

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2018, 7:31:39 PM Β· Difficulty 11.6930 Β· 4,159,021 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2a30b54b9e4688acceb74287b9e8bba505edd6f4ff4a7074adb0ff650803002
View on Chainz β†—

Difficulty

11.693044

Transactions

1

Size

201 B

Version

2

Bits

0bb16b59

Nonce

1,285,187,855

Timestamp

5/26/2018, 7:31:39 PM

Confirmations

4,159,021

Merkle Root

0fdff3a55f5c8959df8cd47915f3d40253b10d0836deb51873769c7d09d71199
Transactions (1)
Coinbase0fdff3a55f5c89…769c7d09d71199
1 in β†’ 1 out7.3000 XPM110 B
ARdTfr3j…YZCKc4ki
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.

4.374 Γ— 10⁹⁷(98-digit number)
43748135581887724799…89619372921536266240
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
4.374 Γ— 10⁹⁷(98-digit number)
43748135581887724799…89619372921536266241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.749 Γ— 10⁹⁷(98-digit number)
87496271163775449599…79238745843072532481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.749 Γ— 10⁹⁸(99-digit number)
17499254232755089919…58477491686145064961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.499 Γ— 10⁹⁸(99-digit number)
34998508465510179839…16954983372290129921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.999 Γ— 10⁹⁸(99-digit number)
69997016931020359679…33909966744580259841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.399 Γ— 10⁹⁹(100-digit number)
13999403386204071935…67819933489160519681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.799 Γ— 10⁹⁹(100-digit number)
27998806772408143871…35639866978321039361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.599 Γ— 10⁹⁹(100-digit number)
55997613544816287743…71279733956642078721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.119 Γ— 10¹⁰⁰(101-digit number)
11199522708963257548…42559467913284157441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.239 Γ— 10¹⁰⁰(101-digit number)
22399045417926515097…85118935826568314881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.479 Γ— 10¹⁰⁰(101-digit number)
44798090835853030195…70237871653136629761
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 2679141

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 d2a30b54b9e4688acceb74287b9e8bba505edd6f4ff4a7074adb0ff650803002

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 #2,679,141 on Chainz β†—
Circulating Supply:57,949,568 XPMΒ·at block #6,838,161 Β· updates every 60s
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