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Home/Chain Registry/Block #103,837

Block #103,837

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 6:42:03 PM Β· Difficulty 9.5393 Β· 6,690,957 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e90aafd70899ad5d177d03fc2302a08493d20590696532900d9d38858d681d8
View on Chainz β†—

Height

#103,837

Difficulty

9.539274

Transactions

1

Size

201 B

Version

2

Bits

098a0dd7

Nonce

196,450

Timestamp

8/7/2013, 6:42:03 PM

Confirmations

6,690,957

Merkle Root

100336a2838a388197918f515853dca11c08bf688d5c4112dea2c76437ec40f2
Transactions (1)
Coinbase100336a2838a38…a2c76437ec40f2
1 in β†’ 1 out10.9700 XPM109 B
AcgKcpD7…9rx6iFP6
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.

1.749 Γ— 10⁹⁸(99-digit number)
17499333390033622760…47496894953472744800
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
1.749 Γ— 10⁹⁸(99-digit number)
17499333390033622760…47496894953472744801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.499 Γ— 10⁹⁸(99-digit number)
34998666780067245521…94993789906945489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.999 Γ— 10⁹⁸(99-digit number)
69997333560134491043…89987579813890979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.399 Γ— 10⁹⁹(100-digit number)
13999466712026898208…79975159627781958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.799 Γ— 10⁹⁹(100-digit number)
27998933424053796417…59950319255563916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.599 Γ— 10⁹⁹(100-digit number)
55997866848107592834…19900638511127833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.119 Γ— 10¹⁰⁰(101-digit number)
11199573369621518566…39801277022255667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.239 Γ— 10¹⁰⁰(101-digit number)
22399146739243037133…79602554044511334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.479 Γ— 10¹⁰⁰(101-digit number)
44798293478486074267…59205108089022668801
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 103837

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 7e90aafd70899ad5d177d03fc2302a08493d20590696532900d9d38858d681d8

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 #103,837 on Chainz β†—
Circulating Supply:57,602,406 XPMΒ·at block #6,794,793 Β· updates every 60s
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