Home/Chain Registry/Block #410,210

Block #410,210

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/18/2014, 10:07:31 PM · Difficulty 10.4281 · 6,416,995 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

be693544cca29e38d6bd7a8cb99d95431076dd97b1dd744342affce0afdaf65a

View on Chainz ↗

Height

#410,210

Difficulty

10.428127

Transactions

Size

1.53 KB

Version

Bits

0a6d99c3

Nonce

702

Timestamp

2/18/2014, 10:07:31 PM

Confirmations

6,416,995

Merkle Root

b49077ac092c58e7609a9b6f1fac3074336d4323cc22c37ca263e9e3a4126617

Transactions (3)

Coinbased775303b359305…d255fc4de310cc

1 in → 24 out9.2042 XPM879 B

AVX58G34…Ywdo7n2q AMypZdXS…5jJKu8wP Acs9SHrk…QJSB8SFG AXCBfU18…vZFjKTCm AbPcCMg4…719q6mAX

fe95396f825f1e…a201e00a7e230f

2 in → 4 out12.4103 XPM407 B

AUmVQTQX…dRuD9hP5 Ad4XAfRG…ePHYewUC ALvVMKLt…wbxp4TJH AeKNrjNj…1NEq95Ta

a17b9bfdb775f8…fb7cfc33ec4a2e

1 in → 1 out2.9900 XPM192 B

ANwqVoXC…YY23SfmD

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.874 × 10¹⁰¹(102-digit number)

18748085144868716164…93318688710959979520

Discovered Prime Numbers

p_k = 2^k × origin − 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.

origin − 1

1.874 × 10¹⁰¹(102-digit number)

18748085144868716164…93318688710959979519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.749 × 10¹⁰¹(102-digit number)

37496170289737432329…86637377421919959039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.499 × 10¹⁰¹(102-digit number)

74992340579474864659…73274754843839918079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.499 × 10¹⁰²(103-digit number)

14998468115894972931…46549509687679836159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.999 × 10¹⁰²(103-digit number)

29996936231789945863…93099019375359672319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.999 × 10¹⁰²(103-digit number)

59993872463579891727…86198038750719344639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.199 × 10¹⁰³(104-digit number)

11998774492715978345…72396077501438689279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.399 × 10¹⁰³(104-digit number)

23997548985431956691…44792155002877378559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.799 × 10¹⁰³(104-digit number)

47995097970863913382…89584310005754757119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.599 × 10¹⁰³(104-digit number)

95990195941727826764…79168620011509514239

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — 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 →

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 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 410210

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 be693544cca29e38d6bd7a8cb99d95431076dd97b1dd744342affce0afdaf65a

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 → Debug Window → 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 #410,210 on Chainz ↗

Block #410,210

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