Block #393,703

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/7/2014, 8:44:53 AM · Difficulty 10.4364 · 6,405,652 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

09a88bc5a57a36274a67895689cce42db23a65f4fd9c49e3e74b036a3a4fcd7a

View on Chainz ↗

Height

#393,703

Difficulty

10.436379

Transactions

Size

798 B

Version

Bits

0a6fb683

Nonce

29,883

Timestamp

2/7/2014, 8:44:53 AM

Confirmations

6,405,652

Mined by

⛏️ .HZAbPcCMg4L29d17fPXxDc6v13Qy719q6mAX

Merkle Root

cfed7c639f976dadd2d4544073145e0230b34aea929f92facd390831bdf867fc

Transactions (1)

Coinbasecfed7c639f976d…390831bdf867fc

1 in → 19 out9.1700 XPM709 B

AbPcCMg4…719q6mAX Acs9SHrk…QJSB8SFG AMunqLwt…nFnv4dvR AW2fas42…gGAHYdHj AHg2Vvtk…kKAH15JW

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.

1.208 × 10⁹³(94-digit number)

12083746050245094091…93014157250991583999

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

1.208 × 10⁹³(94-digit number)

12083746050245094091…93014157250991583999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.416 × 10⁹³(94-digit number)

24167492100490188183…86028314501983167999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.833 × 10⁹³(94-digit number)

48334984200980376367…72056629003966335999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.666 × 10⁹³(94-digit number)

96669968401960752734…44113258007932671999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.933 × 10⁹⁴(95-digit number)

19333993680392150546…88226516015865343999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.866 × 10⁹⁴(95-digit number)

38667987360784301093…76453032031730687999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.733 × 10⁹⁴(95-digit number)

77335974721568602187…52906064063461375999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.546 × 10⁹⁵(96-digit number)

15467194944313720437…05812128126922751999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.093 × 10⁹⁵(96-digit number)

30934389888627440874…11624256253845503999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.186 × 10⁹⁵(96-digit number)

61868779777254881749…23248512507691007999

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