Block #360,884

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/15/2014, 5:26:08 PM · Difficulty 10.4004 · 6,457,140 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cd7a2012af4f27ea4d64e82f2ca9e7f34c8aa2ed88bcd30cb3bce649b2fb6f58

View on Chainz ↗

Height

#360,884

Difficulty

10.400403

Transactions

Size

1003 B

Version

Bits

0a6680d8

Nonce

29,130

Timestamp

1/15/2014, 5:26:08 PM

Confirmations

6,457,140

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2e4497053be5809bbec123c6188457e8e772df3989bf9aaec8c1a37052ce8e95

Transactions (1)

Coinbase2e4497053be580…c1a37052ce8e95

1 in → 25 out9.2300 XPM913 B

AQvZBsUo…hppgRZTJ AQwRN8bE…V8PsTcY9 AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 Ac5JXwCr…tf5C9dQa

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.

3.516 × 10⁹⁴(95-digit number)

35167973445568876242…57678000256354629119

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

3.516 × 10⁹⁴(95-digit number)

35167973445568876242…57678000256354629119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.033 × 10⁹⁴(95-digit number)

70335946891137752484…15356000512709258239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.406 × 10⁹⁵(96-digit number)

14067189378227550496…30712001025418516479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.813 × 10⁹⁵(96-digit number)

28134378756455100993…61424002050837032959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.626 × 10⁹⁵(96-digit number)

56268757512910201987…22848004101674065919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.125 × 10⁹⁶(97-digit number)

11253751502582040397…45696008203348131839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.250 × 10⁹⁶(97-digit number)

22507503005164080795…91392016406696263679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.501 × 10⁹⁶(97-digit number)

45015006010328161590…82784032813392527359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.003 × 10⁹⁶(97-digit number)

90030012020656323180…65568065626785054719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.800 × 10⁹⁷(98-digit number)

18006002404131264636…31136131253570109439

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 #360,884

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