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Block #490,837

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/14/2014, 2:55:42 AM Β· Difficulty 10.6798 Β· 6,335,378 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3d99e2a57cf6a8acd5f02f597611e2656473b9dfeda1d116a3167accc87a1dec
View on Chainz β†—

Height

#490,837

Difficulty

10.679769

Transactions

1

Size

204 B

Version

2

Bits

0aae0551

Nonce

19,774

Timestamp

4/14/2014, 2:55:42 AM

Confirmations

6,335,378

Merkle Root

691a02a1ace7999ab7793c1029a513bf13d582f5b96d2cfa27a5138f492dfc70
Transactions (1)
Coinbase691a02a1ace799…a5138f492dfc70
1 in β†’ 1 out8.7500 XPM112 B
ARQ2Ksxo…cb467zPj
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.

2.589 Γ— 10⁹⁹(100-digit number)
25897536150017670078…65071942927360152960
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
2.589 Γ— 10⁹⁹(100-digit number)
25897536150017670078…65071942927360152959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.179 Γ— 10⁹⁹(100-digit number)
51795072300035340157…30143885854720305919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.035 Γ— 10¹⁰⁰(101-digit number)
10359014460007068031…60287771709440611839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.071 Γ— 10¹⁰⁰(101-digit number)
20718028920014136063…20575543418881223679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.143 Γ— 10¹⁰⁰(101-digit number)
41436057840028272126…41151086837762447359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.287 Γ— 10¹⁰⁰(101-digit number)
82872115680056544252…82302173675524894719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.657 Γ— 10¹⁰¹(102-digit number)
16574423136011308850…64604347351049789439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.314 Γ— 10¹⁰¹(102-digit number)
33148846272022617700…29208694702099578879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.629 Γ— 10¹⁰¹(102-digit number)
66297692544045235401…58417389404199157759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.325 Γ— 10¹⁰²(103-digit number)
13259538508809047080…16834778808398315519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.651 Γ— 10¹⁰²(103-digit number)
26519077017618094160…33669557616796631039
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 490837

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 3d99e2a57cf6a8acd5f02f597611e2656473b9dfeda1d116a3167accc87a1dec

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 #490,837 on Chainz β†—
Circulating Supply:57,853,852 XPMΒ·at block #6,826,214 Β· updates every 60s
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