Block #353,520

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/10/2014, 11:56:31 PM · Difficulty 10.3278 · 6,452,396 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2d2d8256b6685829b570e6ca4969feb4705cb734001fa92f531c767aa2be76e5

View on Chainz ↗

Height

#353,520

Difficulty

10.327845

Transactions

Size

1.08 KB

Version

Bits

0a53eda8

Nonce

266,094

Timestamp

1/10/2014, 11:56:31 PM

Confirmations

6,452,396

Mined by

⛏️ daRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

3b9b02bbdb4086fdd5cdac0a1433b1130ec5489f8ec1426e203cfd377c281ad0

Transactions (1)

Coinbase3b9b02bbdb4086…3cfd377c281ad0

1 in → 28 out9.3400 XPM1015 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz

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.

3.219 × 10⁹⁷(98-digit number)

32192176999203126247…01763601223109382081

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

3.219 × 10⁹⁷(98-digit number)

32192176999203126247…01763601223109382081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.438 × 10⁹⁷(98-digit number)

64384353998406252495…03527202446218764161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.287 × 10⁹⁸(99-digit number)

12876870799681250499…07054404892437528321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.575 × 10⁹⁸(99-digit number)

25753741599362500998…14108809784875056641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.150 × 10⁹⁸(99-digit number)

51507483198725001996…28217619569750113281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.030 × 10⁹⁹(100-digit number)

10301496639745000399…56435239139500226561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.060 × 10⁹⁹(100-digit number)

20602993279490000798…12870478279000453121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.120 × 10⁹⁹(100-digit number)

41205986558980001597…25740956558000906241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.241 × 10⁹⁹(100-digit number)

82411973117960003194…51481913116001812481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.648 × 10¹⁰⁰(101-digit number)

16482394623592000638…02963826232003624961

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 Second 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer