Block #295,207

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/5/2013, 7:40:46 AM · Difficulty 9.9913 · 6,512,389 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7e704f55bcd7f7a03f15a5b1008c0201a72be26560c1c21034e56f35e02cbd41

View on Chainz ↗

Height

#295,207

Difficulty

9.991298

Transactions

Size

1.15 KB

Version

Bits

09fdc5ba

Nonce

18,561

Timestamp

12/5/2013, 7:40:46 AM

Confirmations

6,512,389

Mined by

⛏️ 'aR-AYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

85f1fc3755c11ac7d605c906b632ac7ab60aaef496526c360433a8fc6502d247

Transactions (1)

Coinbase85f1fc3755c11a…33a8fc6502d247

1 in → 30 out9.9800 XPM1.06 KB

AYcLTeXR…bscgPops APeshfYV…3PKcKMKH AToTBTPr…X3DsBU1U ARcqMJhp…RVLToQ6S ASy3AE9X…ghJMwaMJ

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.

2.585 × 10⁹⁴(95-digit number)

25855363285088115470…35227558283610698239

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

2.585 × 10⁹⁴(95-digit number)

25855363285088115470…35227558283610698239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.171 × 10⁹⁴(95-digit number)

51710726570176230940…70455116567221396479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.034 × 10⁹⁵(96-digit number)

10342145314035246188…40910233134442792959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.068 × 10⁹⁵(96-digit number)

20684290628070492376…81820466268885585919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.136 × 10⁹⁵(96-digit number)

41368581256140984752…63640932537771171839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.273 × 10⁹⁵(96-digit number)

82737162512281969504…27281865075542343679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.654 × 10⁹⁶(97-digit number)

16547432502456393900…54563730151084687359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.309 × 10⁹⁶(97-digit number)

33094865004912787801…09127460302169374719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.618 × 10⁹⁶(97-digit number)

66189730009825575603…18254920604338749439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.323 × 10⁹⁷(98-digit number)

13237946001965115120…36509841208677498879

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 #295,207

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