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Home/Chain Registry/Block #2,665,155

Block #2,665,155

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/17/2018, 11:03:54 AM Β· Difficulty 11.6594 Β· 4,176,202 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dacffa76a5880c5af3c13f364b885ff3f9a399220c3f1c8247969223227bc1cb
View on Chainz β†—

Difficulty

11.659384

Transactions

1

Size

201 B

Version

2

Bits

0ba8cd68

Nonce

1,414,441,685

Timestamp

5/17/2018, 11:03:54 AM

Confirmations

4,176,202

Merkle Root

30886d162b9d9880a7015f2cecefd650c2a836ac59c64423950e99e045552fe5
Transactions (1)
Coinbase30886d162b9d98…0e99e045552fe5
1 in β†’ 1 out7.3400 XPM110 B
ATba78Q6…JcRNUtFy
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.

1.200 Γ— 10⁹⁢(97-digit number)
12002784450844536830…82184849927213158400
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
1.200 Γ— 10⁹⁢(97-digit number)
12002784450844536830…82184849927213158401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.400 Γ— 10⁹⁢(97-digit number)
24005568901689073661…64369699854426316801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.801 Γ— 10⁹⁢(97-digit number)
48011137803378147322…28739399708852633601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.602 Γ— 10⁹⁢(97-digit number)
96022275606756294644…57478799417705267201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.920 Γ— 10⁹⁷(98-digit number)
19204455121351258928…14957598835410534401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.840 Γ— 10⁹⁷(98-digit number)
38408910242702517857…29915197670821068801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.681 Γ— 10⁹⁷(98-digit number)
76817820485405035715…59830395341642137601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.536 Γ— 10⁹⁸(99-digit number)
15363564097081007143…19660790683284275201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.072 Γ— 10⁹⁸(99-digit number)
30727128194162014286…39321581366568550401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.145 Γ— 10⁹⁸(99-digit number)
61454256388324028572…78643162733137100801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.229 Γ— 10⁹⁹(100-digit number)
12290851277664805714…57286325466274201601
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 2665155

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 dacffa76a5880c5af3c13f364b885ff3f9a399220c3f1c8247969223227bc1cb

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 #2,665,155 on Chainz β†—
Circulating Supply:57,975,224 XPMΒ·at block #6,841,356 Β· updates every 60s
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