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Block #325,088

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/22/2013, 7:04:50 PM Β· Difficulty 10.2068 Β· 6,489,716 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
def5d4b3d889f14ca69bb97fb767e324309ef3f644f42ef92d43a3d4a4a58ce8
View on Chainz β†—

Height

#325,088

Difficulty

10.206763

Transactions

1

Size

206 B

Version

2

Bits

0a34ee6b

Nonce

403,666

Timestamp

12/22/2013, 7:04:50 PM

Confirmations

6,489,716

Merkle Root

599d430a3e67ef39771270cb549581be9668fd3f9200ab93476acbbf2bfb177c
Transactions (1)
Coinbase599d430a3e67ef…6acbbf2bfb177c
1 in β†’ 1 out9.5800 XPM116 B
AbwWkWZt…kawDhufa
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.

2.581 Γ— 10⁹⁡(96-digit number)
25818146826260513056…73067016882611672320
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
2.581 Γ— 10⁹⁡(96-digit number)
25818146826260513056…73067016882611672319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.163 Γ— 10⁹⁡(96-digit number)
51636293652521026112…46134033765223344639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.032 Γ— 10⁹⁢(97-digit number)
10327258730504205222…92268067530446689279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.065 Γ— 10⁹⁢(97-digit number)
20654517461008410444…84536135060893378559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.130 Γ— 10⁹⁢(97-digit number)
41309034922016820889…69072270121786757119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.261 Γ— 10⁹⁢(97-digit number)
82618069844033641779…38144540243573514239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁷(98-digit number)
16523613968806728355…76289080487147028479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.304 Γ— 10⁹⁷(98-digit number)
33047227937613456711…52578160974294056959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.609 Γ— 10⁹⁷(98-digit number)
66094455875226913423…05156321948588113919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.321 Γ— 10⁹⁸(99-digit number)
13218891175045382684…10312643897176227839
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 325088

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 def5d4b3d889f14ca69bb97fb767e324309ef3f644f42ef92d43a3d4a4a58ce8

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 #325,088 on Chainz β†—
Circulating Supply:57,762,517 XPMΒ·at block #6,814,803 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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