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Home/Chain Registry/Block #2,159,785

Block #2,159,785

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/14/2017, 2:34:04 AM Β· Difficulty 10.9027 Β· 4,679,956 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
752d0c3ec77026f37aaf172b925f60f0146ea0990e4a79777725d8dd8c3c506b
View on Chainz β†—

Difficulty

10.902688

Transactions

2

Size

424 B

Version

2

Bits

0ae7168b

Nonce

945,356,904

Timestamp

6/14/2017, 2:34:04 AM

Confirmations

4,679,956

Merkle Root

ebea31e27b77216ad8eccf19ffd2beefdf3f9654217737cd4aff64892c16e09d
Transactions (2)
Coinbase90e3aebbc4c823…1c8f23cd21b7d9
1 in β†’ 1 out8.4100 XPM109 B
AW9FYrDJ…4tGfhoKt
37373b105c91a6…5e31eeec0caa3e
1 in β†’ 2 out2333.0589 XPM225 B
AX67ZToy…3h9CBQ95AMRycWoF…13hkF5ou
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.

2.643 Γ— 10⁹⁡(96-digit number)
26436991872112316501…32195295263458735520
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
2.643 Γ— 10⁹⁡(96-digit number)
26436991872112316501…32195295263458735521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.287 Γ— 10⁹⁡(96-digit number)
52873983744224633002…64390590526917471041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.057 Γ— 10⁹⁢(97-digit number)
10574796748844926600…28781181053834942081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.114 Γ— 10⁹⁢(97-digit number)
21149593497689853200…57562362107669884161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.229 Γ— 10⁹⁢(97-digit number)
42299186995379706401…15124724215339768321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.459 Γ— 10⁹⁢(97-digit number)
84598373990759412803…30249448430679536641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.691 Γ— 10⁹⁷(98-digit number)
16919674798151882560…60498896861359073281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.383 Γ— 10⁹⁷(98-digit number)
33839349596303765121…20997793722718146561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.767 Γ— 10⁹⁷(98-digit number)
67678699192607530242…41995587445436293121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.353 Γ— 10⁹⁸(99-digit number)
13535739838521506048…83991174890872586241
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 2159785

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 752d0c3ec77026f37aaf172b925f60f0146ea0990e4a79777725d8dd8c3c506b

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 #2,159,785 on Chainz β†—
Circulating Supply:57,962,214 XPMΒ·at block #6,839,740 Β· updates every 60s
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