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Block #208,157

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/13/2013, 8:44:58 PM Β· Difficulty 9.9051 Β· 6,587,152 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2c41fdcda333fad4a4b9f02bee95bfed26733bff9f0e9b25aec5e12ae9a67a8c
View on Chainz β†—

Height

#208,157

Difficulty

9.905133

Transactions

1

Size

199 B

Version

2

Bits

09e7b6cc

Nonce

26,488

Timestamp

10/13/2013, 8:44:58 PM

Confirmations

6,587,152

Merkle Root

71259c1c66e8348f5a4955c4212ddcfdae03efa54f399a32e22fa8cf91f498c0
Transactions (1)
Coinbase71259c1c66e834…2fa8cf91f498c0
1 in β†’ 1 out10.1800 XPM109 B
AdXUCdqw…gYZcJpLP
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.

7.730 Γ— 10⁹³(94-digit number)
77308795375358074418…88722121168328162080
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
7.730 Γ— 10⁹³(94-digit number)
77308795375358074418…88722121168328162081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.546 Γ— 10⁹⁴(95-digit number)
15461759075071614883…77444242336656324161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.092 Γ— 10⁹⁴(95-digit number)
30923518150143229767…54888484673312648321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.184 Γ— 10⁹⁴(95-digit number)
61847036300286459534…09776969346625296641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.236 Γ— 10⁹⁡(96-digit number)
12369407260057291906…19553938693250593281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.473 Γ— 10⁹⁡(96-digit number)
24738814520114583813…39107877386501186561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.947 Γ— 10⁹⁡(96-digit number)
49477629040229167627…78215754773002373121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.895 Γ— 10⁹⁡(96-digit number)
98955258080458335255…56431509546004746241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.979 Γ— 10⁹⁢(97-digit number)
19791051616091667051…12863019092009492481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.958 Γ— 10⁹⁢(97-digit number)
39582103232183334102…25726038184018984961
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 208157

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 2c41fdcda333fad4a4b9f02bee95bfed26733bff9f0e9b25aec5e12ae9a67a8c

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 #208,157 on Chainz β†—
Circulating Supply:57,606,526 XPMΒ·at block #6,795,308 Β· updates every 60s
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