Block #601,999

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/25/2014, 11:21:24 PM · Difficulty 10.9139 · 6,197,493 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a06b3da7050e4f1838332581e19a8ec5548277b629be28a4ca2e54ee0d3f7205

View on Chainz ↗

Height

#601,999

Difficulty

10.913879

Transactions

Size

765 B

Version

Bits

0ae9f3f8

Nonce

203,728

Timestamp

6/25/2014, 11:21:24 PM

Confirmations

6,197,493

Mined by

⛏️ aSYxAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1ea9cafa85ca4e2f1b68c9e98065d9c43e9e6e1bc482046485575572c9818624

Transactions (1)

Coinbase1ea9cafa85ca4e…575572c9818624

1 in → 18 out8.3800 XPM675 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn AVqfVWKX…SP4z6pCB

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.

1.850 × 10⁹⁵(96-digit number)

18508163535676299828…41027828358485657601

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

1.850 × 10⁹⁵(96-digit number)

18508163535676299828…41027828358485657601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.701 × 10⁹⁵(96-digit number)

37016327071352599657…82055656716971315201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.403 × 10⁹⁵(96-digit number)

74032654142705199314…64111313433942630401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.480 × 10⁹⁶(97-digit number)

14806530828541039862…28222626867885260801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.961 × 10⁹⁶(97-digit number)

29613061657082079725…56445253735770521601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.922 × 10⁹⁶(97-digit number)

59226123314164159451…12890507471541043201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.184 × 10⁹⁷(98-digit number)

11845224662832831890…25781014943082086401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.369 × 10⁹⁷(98-digit number)

23690449325665663780…51562029886164172801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.738 × 10⁹⁷(98-digit number)

47380898651331327561…03124059772328345601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.476 × 10⁹⁷(98-digit number)

94761797302662655122…06248119544656691201

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