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Home/Chain Registry/Block #2,925,385

Block #2,925,385

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/16/2018, 12:16:53 PM Β· Difficulty 11.3535 Β· 3,916,580 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e3493ed4e7735d7c3c42f37f35f8a830529de7cae4c2ef79c6a0ed5a9c42435e
View on Chainz β†—

Difficulty

11.353476

Transactions

1

Size

200 B

Version

2

Bits

0b5a7d61

Nonce

592,856,464

Timestamp

11/16/2018, 12:16:53 PM

Confirmations

3,916,580

Merkle Root

e5c1b4040110ca1e47c43689f87f5bdd2263220741602594dd466b33831d7d72
Transactions (1)
Coinbasee5c1b4040110ca…466b33831d7d72
1 in β†’ 1 out7.7500 XPM109 B
AUMQRepm…tAfKmdW1
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.

1.965 Γ— 10⁹⁢(97-digit number)
19651427184373878580…46871244211332304640
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
1.965 Γ— 10⁹⁢(97-digit number)
19651427184373878580…46871244211332304641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.930 Γ— 10⁹⁢(97-digit number)
39302854368747757160…93742488422664609281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.860 Γ— 10⁹⁢(97-digit number)
78605708737495514321…87484976845329218561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.572 Γ— 10⁹⁷(98-digit number)
15721141747499102864…74969953690658437121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.144 Γ— 10⁹⁷(98-digit number)
31442283494998205728…49939907381316874241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.288 Γ— 10⁹⁷(98-digit number)
62884566989996411456…99879814762633748481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.257 Γ— 10⁹⁸(99-digit number)
12576913397999282291…99759629525267496961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.515 Γ— 10⁹⁸(99-digit number)
25153826795998564582…99519259050534993921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.030 Γ— 10⁹⁸(99-digit number)
50307653591997129165…99038518101069987841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.006 Γ— 10⁹⁹(100-digit number)
10061530718399425833…98077036202139975681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.012 Γ— 10⁹⁹(100-digit number)
20123061436798851666…96154072404279951361
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 2925385

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 e3493ed4e7735d7c3c42f37f35f8a830529de7cae4c2ef79c6a0ed5a9c42435e

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 #2,925,385 on Chainz β†—
Circulating Supply:57,980,102 XPMΒ·at block #6,841,964 Β· updates every 60s
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