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Block #136,092

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2013, 12:26:54 AM Β· Difficulty 9.8144 Β· 6,691,067 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f788bf10f707275b94f72b1dc233df293c8ec5a915e4008f6447cea810bf530
View on Chainz β†—

Height

#136,092

Difficulty

9.814360

Transactions

1

Size

197 B

Version

2

Bits

09d079ed

Nonce

119,157

Timestamp

8/27/2013, 12:26:54 AM

Confirmations

6,691,067

Merkle Root

fd6f513fca5cd5978fba24437e34a6c128bb92abb3f5a0d21f4840cca36199d0
Transactions (1)
Coinbasefd6f513fca5cd5…4840cca36199d0
1 in β†’ 1 out10.3700 XPM109 B
AY88KHST…88L8yacq
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.

1.393 Γ— 10⁸⁹(90-digit number)
13930030750923541420…66634808647544569400
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
1.393 Γ— 10⁸⁹(90-digit number)
13930030750923541420…66634808647544569401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.786 Γ— 10⁸⁹(90-digit number)
27860061501847082840…33269617295089138801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.572 Γ— 10⁸⁹(90-digit number)
55720123003694165680…66539234590178277601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.114 Γ— 10⁹⁰(91-digit number)
11144024600738833136…33078469180356555201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.228 Γ— 10⁹⁰(91-digit number)
22288049201477666272…66156938360713110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.457 Γ— 10⁹⁰(91-digit number)
44576098402955332544…32313876721426220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.915 Γ— 10⁹⁰(91-digit number)
89152196805910665089…64627753442852441601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.783 Γ— 10⁹¹(92-digit number)
17830439361182133017…29255506885704883201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.566 Γ— 10⁹¹(92-digit number)
35660878722364266035…58511013771409766401
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 136092

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 3f788bf10f707275b94f72b1dc233df293c8ec5a915e4008f6447cea810bf530

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 #136,092 on Chainz β†—
Circulating Supply:57,861,457 XPMΒ·at block #6,827,158 Β· updates every 60s
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