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Block #157,030

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 8:48:05 AM Β· Difficulty 9.8687 Β· 6,648,084 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
43cee6138e2d2c2521b3c7fcd3a2044963aaa2f853ee66ea81f01c4dd947caec
View on Chainz β†—

Height

#157,030

Difficulty

9.868720

Transactions

1

Size

202 B

Version

2

Bits

09de646b

Nonce

16,778,374

Timestamp

9/9/2013, 8:48:05 AM

Confirmations

6,648,084

Merkle Root

1a9bdac9aac7e70accfd5ed3aaa01da01a5f32d11c876440696c24b0bf137fd9
Transactions (1)
Coinbase1a9bdac9aac7e7…6c24b0bf137fd9
1 in β†’ 1 out10.2500 XPM112 B
AcLBm5Z9…S683d7c3
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.

2.100 Γ— 10⁹⁴(95-digit number)
21002929735011749017…80379630031322428480
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
2.100 Γ— 10⁹⁴(95-digit number)
21002929735011749017…80379630031322428481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.200 Γ— 10⁹⁴(95-digit number)
42005859470023498035…60759260062644856961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.401 Γ— 10⁹⁴(95-digit number)
84011718940046996071…21518520125289713921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.680 Γ— 10⁹⁡(96-digit number)
16802343788009399214…43037040250579427841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.360 Γ— 10⁹⁡(96-digit number)
33604687576018798428…86074080501158855681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.720 Γ— 10⁹⁡(96-digit number)
67209375152037596856…72148161002317711361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.344 Γ— 10⁹⁢(97-digit number)
13441875030407519371…44296322004635422721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.688 Γ— 10⁹⁢(97-digit number)
26883750060815038742…88592644009270845441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.376 Γ— 10⁹⁢(97-digit number)
53767500121630077485…77185288018541690881
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 157030

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 43cee6138e2d2c2521b3c7fcd3a2044963aaa2f853ee66ea81f01c4dd947caec

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 #157,030 on Chainz β†—
Circulating Supply:57,684,981 XPMΒ·at block #6,805,113 Β· updates every 60s
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