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Block #2,690,970

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/4/2018, 2:39:55 AM Β· Difficulty 11.6861 Β· 4,152,566 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
40f280453c35929486f7eb80d12b6f72be47cba67d9779a963082b253181ba47
View on Chainz β†—

Difficulty

11.686072

Transactions

1

Size

201 B

Version

2

Bits

0bafa263

Nonce

2,061,320,090

Timestamp

6/4/2018, 2:39:55 AM

Confirmations

4,152,566

Merkle Root

04ce4791d3507cadde7fdc9561613daa38b8295d76a1280ff2fb2f0f7be7213e
Transactions (1)
Coinbase04ce4791d3507c…fb2f0f7be7213e
1 in β†’ 1 out7.3100 XPM110 B
AUyDWSeY…bPKkZVqY
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.

1.265 Γ— 10⁹⁷(98-digit number)
12656094928077864675…99252133012767114240
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
1.265 Γ— 10⁹⁷(98-digit number)
12656094928077864675…99252133012767114241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.531 Γ— 10⁹⁷(98-digit number)
25312189856155729350…98504266025534228481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.062 Γ— 10⁹⁷(98-digit number)
50624379712311458700…97008532051068456961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.012 Γ— 10⁹⁸(99-digit number)
10124875942462291740…94017064102136913921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.024 Γ— 10⁹⁸(99-digit number)
20249751884924583480…88034128204273827841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.049 Γ— 10⁹⁸(99-digit number)
40499503769849166960…76068256408547655681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.099 Γ— 10⁹⁸(99-digit number)
80999007539698333921…52136512817095311361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.619 Γ— 10⁹⁹(100-digit number)
16199801507939666784…04273025634190622721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.239 Γ— 10⁹⁹(100-digit number)
32399603015879333568…08546051268381245441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.479 Γ— 10⁹⁹(100-digit number)
64799206031758667137…17092102536762490881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.295 Γ— 10¹⁰⁰(101-digit number)
12959841206351733427…34184205073524981761
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 2690970

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 40f280453c35929486f7eb80d12b6f72be47cba67d9779a963082b253181ba47

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 #2,690,970 on Chainz β†—
Circulating Supply:57,992,663 XPMΒ·at block #6,843,535 Β· updates every 60s
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