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Block #490,762

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/14/2014, 1:47:46 AM Β· Difficulty 10.6792 Β· 6,336,384 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4f60715ba0ea7edacdd6f47a7c6e3decdb3bfdd23ff81be5c0f49c3e8f8b8479
View on Chainz β†—

Height

#490,762

Difficulty

10.679220

Transactions

1

Size

207 B

Version

2

Bits

0aade165

Nonce

94,756,442

Timestamp

4/14/2014, 1:47:46 AM

Confirmations

6,336,384

Merkle Root

c8b2a443b411b20921325bb048a80d936850ac78b6652a6ff6ca8f4be0faf6ab
Transactions (1)
Coinbasec8b2a443b411b2…ca8f4be0faf6ab
1 in β†’ 1 out8.7500 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.

1.688 Γ— 10⁹⁷(98-digit number)
16888936214972686093…62981952153454400800
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
1.688 Γ— 10⁹⁷(98-digit number)
16888936214972686093…62981952153454400799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.377 Γ— 10⁹⁷(98-digit number)
33777872429945372186…25963904306908801599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.755 Γ— 10⁹⁷(98-digit number)
67555744859890744373…51927808613817603199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.351 Γ— 10⁹⁸(99-digit number)
13511148971978148874…03855617227635206399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.702 Γ— 10⁹⁸(99-digit number)
27022297943956297749…07711234455270412799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.404 Γ— 10⁹⁸(99-digit number)
54044595887912595498…15422468910540825599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁹(100-digit number)
10808919177582519099…30844937821081651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.161 Γ— 10⁹⁹(100-digit number)
21617838355165038199…61689875642163302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.323 Γ— 10⁹⁹(100-digit number)
43235676710330076399…23379751284326604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.647 Γ— 10⁹⁹(100-digit number)
86471353420660152798…46759502568653209599
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 490762

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 4f60715ba0ea7edacdd6f47a7c6e3decdb3bfdd23ff81be5c0f49c3e8f8b8479

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 #490,762 on Chainz β†—
Circulating Supply:57,861,351 XPMΒ·at block #6,827,145 Β· updates every 60s
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