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Block #898,249

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/17/2015, 4:21:12 AM Β· Difficulty 10.9443 Β· 5,928,682 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e673cb9bbef3a25e3737114fc5ee365094e32c169c4625d9ff36bacdc61e6394
View on Chainz β†—

Height

#898,249

Difficulty

10.944340

Transactions

1

Size

207 B

Version

2

Bits

0af1c047

Nonce

491,561,067

Timestamp

1/17/2015, 4:21:12 AM

Confirmations

5,928,682

Merkle Root

d9e127640f122647d18b2b0792008bd08ab040d44ff144da7437a9be7c925c1e
Transactions (1)
Coinbased9e127640f1226…37a9be7c925c1e
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.649 Γ— 10⁹⁷(98-digit number)
16497230246037750570…44720478942860625920
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
1.649 Γ— 10⁹⁷(98-digit number)
16497230246037750570…44720478942860625919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.299 Γ— 10⁹⁷(98-digit number)
32994460492075501141…89440957885721251839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.598 Γ— 10⁹⁷(98-digit number)
65988920984151002283…78881915771442503679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.319 Γ— 10⁹⁸(99-digit number)
13197784196830200456…57763831542885007359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.639 Γ— 10⁹⁸(99-digit number)
26395568393660400913…15527663085770014719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.279 Γ— 10⁹⁸(99-digit number)
52791136787320801826…31055326171540029439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.055 Γ— 10⁹⁹(100-digit number)
10558227357464160365…62110652343080058879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.111 Γ— 10⁹⁹(100-digit number)
21116454714928320730…24221304686160117759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.223 Γ— 10⁹⁹(100-digit number)
42232909429856641461…48442609372320235519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.446 Γ— 10⁹⁹(100-digit number)
84465818859713282922…96885218744640471039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.689 Γ— 10¹⁰⁰(101-digit number)
16893163771942656584…93770437489280942079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 898249

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 e673cb9bbef3a25e3737114fc5ee365094e32c169c4625d9ff36bacdc61e6394

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 #898,249 on Chainz β†—
Circulating Supply:57,859,620 XPMΒ·at block #6,826,930 Β· updates every 60s
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