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Block #2,090,853

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2017, 1:37:44 AM Β· Difficulty 10.8741 Β· 4,752,405 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ad61d87250c3cdbdd6cfabf7e6c984022b1023bcaf8cdbf2b4146b4ac5652631
View on Chainz β†—

Difficulty

10.874057

Transactions

1

Size

199 B

Version

2

Bits

0adfc230

Nonce

881,359,697

Timestamp

4/28/2017, 1:37:44 AM

Confirmations

4,752,405

Merkle Root

9991ff6722ca8a2a5f3781fabf9f43eadc009a552dc3e8a64fe8131ffef35864
Transactions (1)
Coinbase9991ff6722ca8a…e8131ffef35864
1 in β†’ 1 out8.4400 XPM109 B
AS3DmMH6…YDc1hbM2
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.

8.686 Γ— 10⁹⁴(95-digit number)
86868747940730461739…48475215523688124320
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
8.686 Γ— 10⁹⁴(95-digit number)
86868747940730461739…48475215523688124321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.737 Γ— 10⁹⁡(96-digit number)
17373749588146092347…96950431047376248641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.474 Γ— 10⁹⁡(96-digit number)
34747499176292184695…93900862094752497281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.949 Γ— 10⁹⁡(96-digit number)
69494998352584369391…87801724189504994561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.389 Γ— 10⁹⁢(97-digit number)
13898999670516873878…75603448379009989121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.779 Γ— 10⁹⁢(97-digit number)
27797999341033747756…51206896758019978241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.559 Γ— 10⁹⁢(97-digit number)
55595998682067495513…02413793516039956481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.111 Γ— 10⁹⁷(98-digit number)
11119199736413499102…04827587032079912961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.223 Γ— 10⁹⁷(98-digit number)
22238399472826998205…09655174064159825921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.447 Γ— 10⁹⁷(98-digit number)
44476798945653996410…19310348128319651841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2090853

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 ad61d87250c3cdbdd6cfabf7e6c984022b1023bcaf8cdbf2b4146b4ac5652631

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 #2,090,853 on Chainz β†—
Circulating Supply:57,990,437 XPMΒ·at block #6,843,257 Β· updates every 60s
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