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Block #99,455

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/5/2013, 5:00:42 PM Β· Difficulty 9.3876 Β· 6,717,521 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3ba909ba740fdab738b281e8fecbc0cc57c0490096b6ff1e14902670770b44db
View on Chainz β†—

Height

#99,455

Difficulty

9.387589

Transactions

1

Size

201 B

Version

2

Bits

0963390b

Nonce

91,178

Timestamp

8/5/2013, 5:00:42 PM

Confirmations

6,717,521

Merkle Root

561e25eca11116e780e4316234e5ae3392ea9b6eab7f7a284432b0e9e01f90c0
Transactions (1)
Coinbase561e25eca11116…32b0e9e01f90c0
1 in β†’ 1 out11.3300 XPM109 B
AHdUSd3o…zS6hWpKK
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.

2.813 Γ— 10⁹⁸(99-digit number)
28134659012603501752…32759540862625721740
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
2.813 Γ— 10⁹⁸(99-digit number)
28134659012603501752…32759540862625721739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.626 Γ— 10⁹⁸(99-digit number)
56269318025207003504…65519081725251443479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁹(100-digit number)
11253863605041400700…31038163450502886959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.250 Γ— 10⁹⁹(100-digit number)
22507727210082801401…62076326901005773919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.501 Γ— 10⁹⁹(100-digit number)
45015454420165602803…24152653802011547839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.003 Γ— 10⁹⁹(100-digit number)
90030908840331205607…48305307604023095679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.800 Γ— 10¹⁰⁰(101-digit number)
18006181768066241121…96610615208046191359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.601 Γ— 10¹⁰⁰(101-digit number)
36012363536132482242…93221230416092382719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.202 Γ— 10¹⁰⁰(101-digit number)
72024727072264964485…86442460832184765439
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 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
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 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 99455

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 3ba909ba740fdab738b281e8fecbc0cc57c0490096b6ff1e14902670770b44db

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 #99,455 on Chainz β†—
Circulating Supply:57,779,846 XPMΒ·at block #6,816,975 Β· updates every 60s
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