Home/Chain Registry/Block #31,150

Block #31,150

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/13/2013, 10:13:50 PM · Difficulty 7.9882 · 6,769,061 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

73e08144a4d83d5e41c138157c33e57014d86c66be754399d25ad6c340f87ecf

View on Chainz ↗

Height

#31,150

Difficulty

7.988189

Transactions

Size

545 B

Version

Bits

07fcf9ed

Nonce

310

Timestamp

7/13/2013, 10:13:50 PM

Confirmations

6,769,061

Merkle Root

e9aadb7535e45ccc8d0072c57dc648caf3d0d206c711d4862a55933a4f81072d

Transactions (3)

Coinbase0344cf11e245e3…92e36ea4e4db62

1 in → 1 out15.6700 XPM108 B

AWdtCUuJ…HscHZriH

3e2eaf9669cf2c…91bc5002389d6b

1 in → 2 out15.7800 XPM192 B

ARN2QpX5…mJYRy6BD Aetc3fK3…SdA54VpW

0015021cbb305d…99b0a42ff53e7c

1 in → 1 out15.6700 XPM158 B

ANBXgfaf…ZXqNYSdt

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.

2.003 × 10⁸⁷(88-digit number)

20031592723185826857…50612835928494894500

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

2.003 × 10⁸⁷(88-digit number)

20031592723185826857…50612835928494894499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.006 × 10⁸⁷(88-digit number)

40063185446371653714…01225671856989788999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.012 × 10⁸⁷(88-digit number)

80126370892743307429…02451343713979577999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.602 × 10⁸⁸(89-digit number)

16025274178548661485…04902687427959155999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.205 × 10⁸⁸(89-digit number)

32050548357097322971…09805374855918311999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.410 × 10⁸⁸(89-digit number)

64101096714194645943…19610749711836623999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.282 × 10⁸⁹(90-digit number)

12820219342838929188…39221499423673247999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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

CommonChain length 7

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 31150

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 73e08144a4d83d5e41c138157c33e57014d86c66be754399d25ad6c340f87ecf

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 #31,150 on Chainz ↗