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Block #103,540

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2013, 3:38:03 PM Β· Difficulty 9.5287 Β· 6,722,693 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c6965527dc5c52ac0ec3fe315183888af9aa8e1babf6ca328f8ad9a6c9618a4c
View on Chainz β†—

Height

#103,540

Difficulty

9.528748

Transactions

1

Size

201 B

Version

2

Bits

09875c05

Nonce

274,718

Timestamp

8/7/2013, 3:38:03 PM

Confirmations

6,722,693

Merkle Root

8ea666091510aa80f52307432431dafd40b53b72bef13dda7e0b8fa24c5c2f09
Transactions (1)
Coinbase8ea666091510aa…0b8fa24c5c2f09
1 in β†’ 1 out11.0000 XPM109 B
AKv9qEHV…nw3JmpE2
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.

2.432 Γ— 10⁹⁸(99-digit number)
24322112315436477260…87115765287342984700
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
2.432 Γ— 10⁹⁸(99-digit number)
24322112315436477260…87115765287342984701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.864 Γ— 10⁹⁸(99-digit number)
48644224630872954520…74231530574685969401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.728 Γ— 10⁹⁸(99-digit number)
97288449261745909040…48463061149371938801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.945 Γ— 10⁹⁹(100-digit number)
19457689852349181808…96926122298743877601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.891 Γ— 10⁹⁹(100-digit number)
38915379704698363616…93852244597487755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.783 Γ— 10⁹⁹(100-digit number)
77830759409396727232…87704489194975510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.556 Γ— 10¹⁰⁰(101-digit number)
15566151881879345446…75408978389951020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.113 Γ— 10¹⁰⁰(101-digit number)
31132303763758690892…50817956779902041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.226 Γ— 10¹⁰⁰(101-digit number)
62264607527517381785…01635913559804083201
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 103540

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 c6965527dc5c52ac0ec3fe315183888af9aa8e1babf6ca328f8ad9a6c9618a4c

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 #103,540 on Chainz β†—
Circulating Supply:57,853,995 XPMΒ·at block #6,826,232 Β· updates every 60s
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