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Block #152,327

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/6/2013, 6:24:04 AM Β· Difficulty 9.8622 Β· 6,658,498 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a944f9e40ef9db8d6fa4e0bd449d6068744e7286c7be16ed023e8d94cd1a627d
View on Chainz β†—

Height

#152,327

Difficulty

9.862172

Transactions

1

Size

198 B

Version

2

Bits

09dcb754

Nonce

238,513

Timestamp

9/6/2013, 6:24:04 AM

Confirmations

6,658,498

Merkle Root

8513aafa494457a5a3f07c3ab3ae2f84b2575a0b3e858546d6c9890a7457c362
Transactions (1)
Coinbase8513aafa494457…c9890a7457c362
1 in β†’ 1 out10.2700 XPM109 B
AGHfPnfw…hTc5o83a
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.

6.811 Γ— 10⁹²(93-digit number)
68112987246209233640…48617462624995458080
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
6.811 Γ— 10⁹²(93-digit number)
68112987246209233640…48617462624995458079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.362 Γ— 10⁹³(94-digit number)
13622597449241846728…97234925249990916159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.724 Γ— 10⁹³(94-digit number)
27245194898483693456…94469850499981832319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.449 Γ— 10⁹³(94-digit number)
54490389796967386912…88939700999963664639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.089 Γ— 10⁹⁴(95-digit number)
10898077959393477382…77879401999927329279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.179 Γ— 10⁹⁴(95-digit number)
21796155918786954765…55758803999854658559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.359 Γ— 10⁹⁴(95-digit number)
43592311837573909530…11517607999709317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.718 Γ— 10⁹⁴(95-digit number)
87184623675147819060…23035215999418634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.743 Γ— 10⁹⁡(96-digit number)
17436924735029563812…46070431998837268479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.487 Γ— 10⁹⁡(96-digit number)
34873849470059127624…92140863997674536959
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 152327

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 a944f9e40ef9db8d6fa4e0bd449d6068744e7286c7be16ed023e8d94cd1a627d

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 #152,327 on Chainz β†—
Circulating Supply:57,730,702 XPMΒ·at block #6,810,824 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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