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Home/Chain Registry/Block #2,681,997

Block #2,681,997

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/28/2018, 7:51:10 PM Β· Difficulty 11.6905 Β· 4,158,951 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dba7fc544a1fc59fdd64dcd207850108daa1aef0aa48cac755b42deed5045736
View on Chainz β†—

Difficulty

11.690504

Transactions

1

Size

201 B

Version

2

Bits

0bb0c4e5

Nonce

21,048,337

Timestamp

5/28/2018, 7:51:10 PM

Confirmations

4,158,951

Merkle Root

c36a8d5934822653c85385963a521911ae2037319c18277a798e7dde3772b9bd
Transactions (1)
Coinbasec36a8d59348226…8e7dde3772b9bd
1 in β†’ 1 out7.3000 XPM110 B
ALSuqGNk…Y6XLYgBV
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.

4.573 Γ— 10⁹⁷(98-digit number)
45737541942067970962…64943260568213606400
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
4.573 Γ— 10⁹⁷(98-digit number)
45737541942067970962…64943260568213606401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.147 Γ— 10⁹⁷(98-digit number)
91475083884135941924…29886521136427212801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.829 Γ— 10⁹⁸(99-digit number)
18295016776827188384…59773042272854425601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.659 Γ— 10⁹⁸(99-digit number)
36590033553654376769…19546084545708851201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.318 Γ— 10⁹⁸(99-digit number)
73180067107308753539…39092169091417702401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.463 Γ— 10⁹⁹(100-digit number)
14636013421461750707…78184338182835404801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.927 Γ— 10⁹⁹(100-digit number)
29272026842923501415…56368676365670809601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.854 Γ— 10⁹⁹(100-digit number)
58544053685847002831…12737352731341619201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.170 Γ— 10¹⁰⁰(101-digit number)
11708810737169400566…25474705462683238401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.341 Γ— 10¹⁰⁰(101-digit number)
23417621474338801132…50949410925366476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.683 Γ— 10¹⁰⁰(101-digit number)
46835242948677602265…01898821850732953601
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 2681997

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 dba7fc544a1fc59fdd64dcd207850108daa1aef0aa48cac755b42deed5045736

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 #2,681,997 on Chainz β†—
Circulating Supply:57,971,938 XPMΒ·at block #6,840,947 Β· updates every 60s
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