Home/Chain Registry/Block #2,802,507

Block #2,802,507

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/20/2018, 6:39:49 PM · Difficulty 11.6703 · 4,037,017 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b5030c7813a0301b7462eae7c6ca4e24490c8677ad24580c8d697c70e9c881e4

View on Chainz ↗

Height

#2,802,507

Difficulty

11.670344

Transactions

Size

1.36 KB

Version

Bits

0bab9baa

Nonce

865,314,038

Timestamp

8/20/2018, 6:39:49 PM

Confirmations

4,037,017

Merkle Root

969a68722a4bbb4f95c3ec44ced86cd15e56cb2d07646759d6f9f5b77bf54391

Transactions (3)

Coinbase8adcd744558c72…f339cba1df7d13

1 in → 1 out7.3500 XPM110 B

ARbh2aw4…4roNsyx2

1c8f95f8aa743d…4b78772cd4fa7c

1 in → 2 out5.9327 XPM227 B

ALZhdepx…XMfJNQyq AcKcnWhx…tpkYoHJ3

4f7e1d4a65b667…b42bfb1c238c2e

6 in → 2 out4.0907 XPM967 B

AY6K1KDA…e21gVBwu AdGFnV3a…o6n2zX3x

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.

2.369 × 10⁹⁵(96-digit number)

23690991172410863757…99017932808450475520

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

2.369 × 10⁹⁵(96-digit number)

23690991172410863757…99017932808450475519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.738 × 10⁹⁵(96-digit number)

47381982344821727515…98035865616900951039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.476 × 10⁹⁵(96-digit number)

94763964689643455031…96071731233801902079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.895 × 10⁹⁶(97-digit number)

18952792937928691006…92143462467603804159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.790 × 10⁹⁶(97-digit number)

37905585875857382012…84286924935207608319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.581 × 10⁹⁶(97-digit number)

75811171751714764024…68573849870415216639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.516 × 10⁹⁷(98-digit number)

15162234350342952804…37147699740830433279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.032 × 10⁹⁷(98-digit number)

30324468700685905609…74295399481660866559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.064 × 10⁹⁷(98-digit number)

60648937401371811219…48590798963321733119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.212 × 10⁹⁸(99-digit number)

12129787480274362243…97181597926643466239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.425 × 10⁹⁸(99-digit number)

24259574960548724487…94363195853286932479

Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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

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 × 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 2802507

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 b5030c7813a0301b7462eae7c6ca4e24490c8677ad24580c8d697c70e9c881e4

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 #2,802,507 on Chainz ↗

Block #2,802,507

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