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Block #134,157

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/25/2013, 9:58:01 PM Β· Difficulty 9.8011 Β· 6,690,669 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bad8ef9fffeae001cf04dc72e076bee3973a7318f4251eb9fbdde0c9370b59eb
View on Chainz β†—

Height

#134,157

Difficulty

9.801101

Transactions

1

Size

198 B

Version

2

Bits

09cd14f4

Nonce

159,543

Timestamp

8/25/2013, 9:58:01 PM

Confirmations

6,690,669

Merkle Root

f19f78d0abbcc232b876bca2d121ca9fa8b55a65fcd0df819a1bf423ff741d53
Transactions (1)
Coinbasef19f78d0abbcc2…1bf423ff741d53
1 in β†’ 1 out10.3900 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.

9.678 Γ— 10⁹²(93-digit number)
96784576059777356172…86214141817486554800
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
9.678 Γ— 10⁹²(93-digit number)
96784576059777356172…86214141817486554801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.935 Γ— 10⁹³(94-digit number)
19356915211955471234…72428283634973109601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.871 Γ— 10⁹³(94-digit number)
38713830423910942468…44856567269946219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.742 Γ— 10⁹³(94-digit number)
77427660847821884937…89713134539892438401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.548 Γ— 10⁹⁴(95-digit number)
15485532169564376987…79426269079784876801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.097 Γ— 10⁹⁴(95-digit number)
30971064339128753975…58852538159569753601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.194 Γ— 10⁹⁴(95-digit number)
61942128678257507950…17705076319139507201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.238 Γ— 10⁹⁡(96-digit number)
12388425735651501590…35410152638279014401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.477 Γ— 10⁹⁡(96-digit number)
24776851471303003180…70820305276558028801
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 134157

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 bad8ef9fffeae001cf04dc72e076bee3973a7318f4251eb9fbdde0c9370b59eb

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 #134,157 on Chainz β†—
Circulating Supply:57,842,687 XPMΒ·at block #6,824,825 Β· updates every 60s
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