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Block #136,046

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/26/2013, 11:51:44 PM Β· Difficulty 9.8140 Β· 6,658,979 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0703d06b94d765c282ccc51e9d71aa082bbfec6d189e7186f6b35ecdedaca1c5
View on Chainz β†—

Height

#136,046

Difficulty

9.813958

Transactions

1

Size

201 B

Version

2

Bits

09d05f91

Nonce

156,145

Timestamp

8/26/2013, 11:51:44 PM

Confirmations

6,658,979

Merkle Root

3d740d234520d5f1e533bcc217540738a88e870e9bd15fcf19c8bb32e51530f8
Transactions (1)
Coinbase3d740d234520d5…c8bb32e51530f8
1 in β†’ 1 out10.3700 XPM109 B
AcuHyuDt…fg9uxern
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.

8.060 Γ— 10⁹⁹(100-digit number)
80605112550291044207…33208906154797162160
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
8.060 Γ— 10⁹⁹(100-digit number)
80605112550291044207…33208906154797162161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.612 Γ— 10¹⁰⁰(101-digit number)
16121022510058208841…66417812309594324321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.224 Γ— 10¹⁰⁰(101-digit number)
32242045020116417682…32835624619188648641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.448 Γ— 10¹⁰⁰(101-digit number)
64484090040232835365…65671249238377297281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.289 Γ— 10¹⁰¹(102-digit number)
12896818008046567073…31342498476754594561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.579 Γ— 10¹⁰¹(102-digit number)
25793636016093134146…62684996953509189121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.158 Γ— 10¹⁰¹(102-digit number)
51587272032186268292…25369993907018378241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.031 Γ— 10¹⁰²(103-digit number)
10317454406437253658…50739987814036756481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.063 Γ— 10¹⁰²(103-digit number)
20634908812874507317…01479975628073512961
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 136046

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 0703d06b94d765c282ccc51e9d71aa082bbfec6d189e7186f6b35ecdedaca1c5

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 #136,046 on Chainz β†—
Circulating Supply:57,604,247 XPMΒ·at block #6,795,024 Β· updates every 60s
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