Block #275,407

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/26/2013, 4:47:37 PM · Difficulty 9.9607 · 6,530,635 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f2903a85d8ead23c313e835b79a0cb9929386997ee74746ae4a65676f3fa7bb1

View on Chainz ↗

Height

#275,407

Difficulty

9.960687

Transactions

Size

3.13 KB

Version

Bits

09f5ef8f

Nonce

7,850

Timestamp

11/26/2013, 4:47:37 PM

Confirmations

6,530,635

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

08f48d9ed310897a241d7c07d635fe36e86c6550c9d256bc725711b97794dcbe

Transactions (3)

Coinbased6ad395abe3489…4c44dfcee56a9e

1 in → 2 out10.1100 XPM141 B

AdGRRh1e…QmctLb24 AU6kq4CL…dQBLvxLp

612030892b34e6…02fc5befd11fd1

15 in → 2 out141.8659 XPM2.24 KB

AQHwqAQm…P95QaB2o AKhJc1Yr…pgsxiVjp

52ffbe6bf05c1a…8f09b0bd13de46

4 in → 2 out25.6360 XPM670 B

AGwgsjYq…uStkb5Vt AVNtXbCv…Mayguo96

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.

1.731 × 10¹⁰³(104-digit number)

17317801027002141230…51568467441063922959

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

1.731 × 10¹⁰³(104-digit number)

17317801027002141230…51568467441063922959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.463 × 10¹⁰³(104-digit number)

34635602054004282460…03136934882127845919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.927 × 10¹⁰³(104-digit number)

69271204108008564921…06273869764255691839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.385 × 10¹⁰⁴(105-digit number)

13854240821601712984…12547739528511383679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.770 × 10¹⁰⁴(105-digit number)

27708481643203425968…25095479057022767359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.541 × 10¹⁰⁴(105-digit number)

55416963286406851937…50190958114045534719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.108 × 10¹⁰⁵(106-digit number)

11083392657281370387…00381916228091069439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.216 × 10¹⁰⁵(106-digit number)

22166785314562740775…00763832456182138879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.433 × 10¹⁰⁵(106-digit number)

44333570629125481550…01527664912364277759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …

Cross-reference on Chainz Explorer