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Home/Chain Registry/Block #103,835

Block #103,835

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 6:40:11 PM Β· Difficulty 9.5393 Β· 6,696,421 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f99ef8117f5a5dd79851ad2a29c7389f37fdefe2d4b6daeb022c63ea5111c6dd
View on Chainz β†—

Height

#103,835

Difficulty

9.539286

Transactions

2

Size

360 B

Version

2

Bits

098a0ea2

Nonce

333,996

Timestamp

8/7/2013, 6:40:11 PM

Confirmations

6,696,421

Merkle Root

3ea773bd961657dd68c0d72cdd7e187a0e850a88ba1c0b1c272ac8fe44b22c32
Transactions (2)
Coinbase8afc5edbd6cca0…5362aed997e9ea
1 in β†’ 1 out10.9800 XPM109 B
Ab4AyuXf…j4KXdiui
d454dc51be8ae7…b491a92f43c5ee
1 in β†’ 1 out11.6100 XPM159 B
AYTevZvJ…n8JMVQpg
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.

2.798 Γ— 10⁹⁹(100-digit number)
27989603588941770256…94671047403443264800
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
2.798 Γ— 10⁹⁹(100-digit number)
27989603588941770256…94671047403443264801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.597 Γ— 10⁹⁹(100-digit number)
55979207177883540513…89342094806886529601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.119 Γ— 10¹⁰⁰(101-digit number)
11195841435576708102…78684189613773059201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.239 Γ— 10¹⁰⁰(101-digit number)
22391682871153416205…57368379227546118401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.478 Γ— 10¹⁰⁰(101-digit number)
44783365742306832410…14736758455092236801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.956 Γ— 10¹⁰⁰(101-digit number)
89566731484613664821…29473516910184473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.791 Γ— 10¹⁰¹(102-digit number)
17913346296922732964…58947033820368947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.582 Γ— 10¹⁰¹(102-digit number)
35826692593845465928…17894067640737894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.165 Γ— 10¹⁰¹(102-digit number)
71653385187690931857…35788135281475788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.433 Γ— 10¹⁰²(103-digit number)
14330677037538186371…71576270562951577601
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 103835

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 f99ef8117f5a5dd79851ad2a29c7389f37fdefe2d4b6daeb022c63ea5111c6dd

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 #103,835 on Chainz β†—
Circulating Supply:57,646,103 XPMΒ·at block #6,800,255 Β· updates every 60s
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