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Block #157,071

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 9:21:24 AM Β· Difficulty 9.8689 Β· 6,648,834 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3911d03c0da0cf100158f6c3b00f555bb0acfe62d0d2e31e96e9d8d8a73d498f
View on Chainz β†—

Height

#157,071

Difficulty

9.868920

Transactions

1

Size

199 B

Version

2

Bits

09de7185

Nonce

294,580

Timestamp

9/9/2013, 9:21:24 AM

Confirmations

6,648,834

Merkle Root

e9ec67632f62f34d26d23e323819f2280e533823533bae2b614b169b1f40ccb0
Transactions (1)
Coinbasee9ec67632f62f3…4b169b1f40ccb0
1 in β†’ 1 out10.2500 XPM109 B
AcGRvBM8…Suy1HPgp
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.

4.045 Γ— 10⁹³(94-digit number)
40451850477586778621…98942448246249258240
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
4.045 Γ— 10⁹³(94-digit number)
40451850477586778621…98942448246249258241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.090 Γ— 10⁹³(94-digit number)
80903700955173557242…97884896492498516481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.618 Γ— 10⁹⁴(95-digit number)
16180740191034711448…95769792984997032961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.236 Γ— 10⁹⁴(95-digit number)
32361480382069422896…91539585969994065921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.472 Γ— 10⁹⁴(95-digit number)
64722960764138845793…83079171939988131841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.294 Γ— 10⁹⁡(96-digit number)
12944592152827769158…66158343879976263681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.588 Γ— 10⁹⁡(96-digit number)
25889184305655538317…32316687759952527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.177 Γ— 10⁹⁡(96-digit number)
51778368611311076635…64633375519905054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.035 Γ— 10⁹⁢(97-digit number)
10355673722262215327…29266751039810109441
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 157071

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 3911d03c0da0cf100158f6c3b00f555bb0acfe62d0d2e31e96e9d8d8a73d498f

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 #157,071 on Chainz β†—
Circulating Supply:57,691,329 XPMΒ·at block #6,805,904 Β· updates every 60s
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