Block #353,868

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/11/2014, 4:57:20 AM · Difficulty 10.3342 · 6,462,942 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

776fc62df73d57e8976f61de443439f9aa6713adfe0368db59d5fb59d21c3963

View on Chainz ↗

Height

#353,868

Difficulty

10.334155

Transactions

Size

208 B

Version

Bits

0a558b35

Nonce

180,372

Timestamp

1/11/2014, 4:57:20 AM

Confirmations

6,462,942

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5c5ed84df1ee7eb7354c8beb8495e3e092b30800606a1808e01fc3d0db5633a1

Transactions (1)

Coinbase5c5ed84df1ee7e…1fc3d0db5633a1

1 in → 1 out9.3500 XPM116 B

AbwWkWZt…kawDhufa

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.

4.299 × 10⁹⁸(99-digit number)

42997683308205733392…46627224129751029759

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

4.299 × 10⁹⁸(99-digit number)

42997683308205733392…46627224129751029759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.599 × 10⁹⁸(99-digit number)

85995366616411466784…93254448259502059519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.719 × 10⁹⁹(100-digit number)

17199073323282293356…86508896519004119039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.439 × 10⁹⁹(100-digit number)

34398146646564586713…73017793038008238079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.879 × 10⁹⁹(100-digit number)

68796293293129173427…46035586076016476159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.375 × 10¹⁰⁰(101-digit number)

13759258658625834685…92071172152032952319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.751 × 10¹⁰⁰(101-digit number)

27518517317251669371…84142344304065904639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.503 × 10¹⁰⁰(101-digit number)

55037034634503338742…68284688608131809279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.100 × 10¹⁰¹(102-digit number)

11007406926900667748…36569377216263618559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.201 × 10¹⁰¹(102-digit number)

22014813853801335496…73138754432527237119

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.

★★☆☆☆

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #353,868

Cookie Preferences