Block #459,435

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/25/2014, 7:46:26 AM · Difficulty 10.4168 · 6,342,958 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

092eb619238f0d6367aeab07220b789d6763d1b71c43eccfcf3645399a85f2fe

View on Chainz ↗

Height

#459,435

Difficulty

10.416779

Transactions

Size

1002 B

Version

Bits

0a6ab20a

Nonce

221

Timestamp

3/25/2014, 7:46:26 AM

Confirmations

6,342,958

Mined by

⛏️ aS14C^AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

be58a5dd874d88655b65ff6618cefb40161a92fa722b4f34c2ef2cd20fd861b8

Transactions (1)

Coinbasebe58a5dd874d88…ef2cd20fd861b8

1 in → 25 out9.2000 XPM913 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j ANNg88pG…ppn21sTe

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.

2.897 × 10⁹³(94-digit number)

28972411212182510802…69804080784500003201

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

2.897 × 10⁹³(94-digit number)

28972411212182510802…69804080784500003201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.794 × 10⁹³(94-digit number)

57944822424365021605…39608161569000006401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.158 × 10⁹⁴(95-digit number)

11588964484873004321…79216323138000012801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.317 × 10⁹⁴(95-digit number)

23177928969746008642…58432646276000025601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.635 × 10⁹⁴(95-digit number)

46355857939492017284…16865292552000051201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.271 × 10⁹⁴(95-digit number)

92711715878984034569…33730585104000102401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.854 × 10⁹⁵(96-digit number)

18542343175796806913…67461170208000204801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.708 × 10⁹⁵(96-digit number)

37084686351593613827…34922340416000409601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.416 × 10⁹⁵(96-digit number)

74169372703187227655…69844680832000819201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.483 × 10⁹⁶(97-digit number)

14833874540637445531…39689361664001638401

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