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Block #147,156

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2013, 10:23:34 PM Β· Difficulty 9.8514 Β· 6,664,875 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3c0ca17fb4a102fcc1b54b99111ba3c8a4fcd7fcdf09e365a68102da1eea5b36
View on Chainz β†—

Height

#147,156

Difficulty

9.851384

Transactions

1

Size

198 B

Version

2

Bits

09d9f449

Nonce

607,184

Timestamp

9/2/2013, 10:23:34 PM

Confirmations

6,664,875

Merkle Root

b98e7828a4dc00da8d53bf43ce65fbdde94713b6ed260f75f59e81dc8aec4975
Transactions (1)
Coinbaseb98e7828a4dc00…9e81dc8aec4975
1 in β†’ 1 out10.2900 XPM109 B
Aa6PpN3X…XAm9RHxt
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.

1.321 Γ— 10⁹³(94-digit number)
13218830571424465550…21205648761795690340
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
1.321 Γ— 10⁹³(94-digit number)
13218830571424465550…21205648761795690341
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.643 Γ— 10⁹³(94-digit number)
26437661142848931100…42411297523591380681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.287 Γ— 10⁹³(94-digit number)
52875322285697862201…84822595047182761361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.057 Γ— 10⁹⁴(95-digit number)
10575064457139572440…69645190094365522721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.115 Γ— 10⁹⁴(95-digit number)
21150128914279144880…39290380188731045441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.230 Γ— 10⁹⁴(95-digit number)
42300257828558289761…78580760377462090881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.460 Γ— 10⁹⁴(95-digit number)
84600515657116579522…57161520754924181761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.692 Γ— 10⁹⁡(96-digit number)
16920103131423315904…14323041509848363521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.384 Γ— 10⁹⁡(96-digit number)
33840206262846631808…28646083019696727041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.768 Γ— 10⁹⁡(96-digit number)
67680412525693263617…57292166039393454081
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 147156

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 3c0ca17fb4a102fcc1b54b99111ba3c8a4fcd7fcdf09e365a68102da1eea5b36

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 #147,156 on Chainz β†—
Circulating Supply:57,740,352 XPMΒ·at block #6,812,030 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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