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Block #298,438

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/7/2013, 8:12:40 AM Β· Difficulty 9.9919 Β· 6,538,340 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de9d447a9858b81b7e5ce402c50aef98929109a6782c4c3aeb8153a9f263b66f
View on Chainz β†—

Height

#298,438

Difficulty

9.991940

Transactions

1

Size

207 B

Version

2

Bits

09fdefc3

Nonce

13,942

Timestamp

12/7/2013, 8:12:40 AM

Confirmations

6,538,340

Merkle Root

25152f8bfabe6f0c2b0f5e3328c0cc640119eedc88bf2224377520489c8dd55e
Transactions (1)
Coinbase25152f8bfabe6f…7520489c8dd55e
1 in β†’ 1 out10.0000 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.

6.681 Γ— 10⁹⁷(98-digit number)
66811873873775428126…52661011415336222720
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
6.681 Γ— 10⁹⁷(98-digit number)
66811873873775428126…52661011415336222719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.336 Γ— 10⁹⁸(99-digit number)
13362374774755085625…05322022830672445439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.672 Γ— 10⁹⁸(99-digit number)
26724749549510171250…10644045661344890879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.344 Γ— 10⁹⁸(99-digit number)
53449499099020342501…21288091322689781759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.068 Γ— 10⁹⁹(100-digit number)
10689899819804068500…42576182645379563519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.137 Γ— 10⁹⁹(100-digit number)
21379799639608137000…85152365290759127039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.275 Γ— 10⁹⁹(100-digit number)
42759599279216274000…70304730581518254079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.551 Γ— 10⁹⁹(100-digit number)
85519198558432548001…40609461163036508159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.710 Γ— 10¹⁰⁰(101-digit number)
17103839711686509600…81218922326073016319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.420 Γ— 10¹⁰⁰(101-digit number)
34207679423373019200…62437844652146032639
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 298438

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 de9d447a9858b81b7e5ce402c50aef98929109a6782c4c3aeb8153a9f263b66f

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 #298,438 on Chainz β†—
Circulating Supply:57,938,502 XPMΒ·at block #6,836,777 Β· updates every 60s
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