Block #343,859

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/4/2014, 10:48:52 PM · Difficulty 10.1854 · 6,452,485 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e214c53b98f506c484b2500246dd27c7771756c48a2d7185bc504706a1a149a1

View on Chainz ↗

Height

#343,859

Difficulty

10.185420

Transactions

Size

1.08 KB

Version

Bits

0a2f77ad

Nonce

268,144

Timestamp

1/4/2014, 10:48:52 PM

Confirmations

6,452,485

Mined by

⛏️ 3?aRAZemWJAowt1PBaxKypgqLxhXgv6jhDtieG

Merkle Root

a2f4f1b3d4a2484b9f4fc8f38bca4d14137b321bbddda71408d0016425bbb42d

Transactions (1)

Coinbasea2f4f1b3d4a248…d0016425bbb42d

1 in → 28 out9.6000 XPM1015 B

AZemWJAo…6jhDtieG AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR AcuM7XiJ…5uND8Jce APJPNQaM…8nyTxzkW

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.

2.426 × 10¹⁰¹(102-digit number)

24260221302118510491…62597933643092284799

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

2.426 × 10¹⁰¹(102-digit number)

24260221302118510491…62597933643092284799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.852 × 10¹⁰¹(102-digit number)

48520442604237020983…25195867286184569599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.704 × 10¹⁰¹(102-digit number)

97040885208474041966…50391734572369139199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.940 × 10¹⁰²(103-digit number)

19408177041694808393…00783469144738278399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.881 × 10¹⁰²(103-digit number)

38816354083389616786…01566938289476556799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.763 × 10¹⁰²(103-digit number)

77632708166779233573…03133876578953113599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.552 × 10¹⁰³(104-digit number)

15526541633355846714…06267753157906227199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.105 × 10¹⁰³(104-digit number)

31053083266711693429…12535506315812454399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.210 × 10¹⁰³(104-digit number)

62106166533423386858…25071012631624908799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.242 × 10¹⁰⁴(105-digit number)

12421233306684677371…50142025263249817599

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