Block #191,914

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/3/2013, 11:54:46 AM · Difficulty 9.8752 · 6,603,810 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e53642c8da3fb627e66b8168440253bd2526401f4652d03e41ff166e2e36d4a5

View on Chainz ↗

Height

#191,914

Difficulty

9.875223

Transactions

Size

3.60 KB

Version

Bits

09e00e9a

Nonce

1,164,915,113

Timestamp

10/3/2013, 11:54:46 AM

Confirmations

6,603,810

Mined by

⛏️ RMZtAauXrWxtQPDhjhTyN7x2r6J4GAMwUoygQt

Merkle Root

3c3a946965be9936405e339fbe0e832c2d371eac9b1ad4752a6d5b29cfdd47cc

Transactions (1)

Coinbase3c3a946965be99…6d5b29cfdd47cc

1 in → 104 out10.2000 XPM3.51 KB

AauXrWxt…MwUoygQt Adrq7bsi…ueGbzWHT AMse1voq…GntYtmba AXAt4Nqf…KCRUrDG2 ARskhKeb…UgDvvX9P

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.

2.958 × 10⁹⁶(97-digit number)

29582516297223292231…29677525672896454779

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

2.958 × 10⁹⁶(97-digit number)

29582516297223292231…29677525672896454779

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.916 × 10⁹⁶(97-digit number)

59165032594446584463…59355051345792909559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.183 × 10⁹⁷(98-digit number)

11833006518889316892…18710102691585819119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.366 × 10⁹⁷(98-digit number)

23666013037778633785…37420205383171638239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.733 × 10⁹⁷(98-digit number)

47332026075557267570…74840410766343276479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.466 × 10⁹⁷(98-digit number)

94664052151114535141…49680821532686552959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.893 × 10⁹⁸(99-digit number)

18932810430222907028…99361643065373105919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.786 × 10⁹⁸(99-digit number)

37865620860445814056…98723286130746211839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.573 × 10⁹⁸(99-digit number)

75731241720891628113…97446572261492423679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.514 × 10⁹⁹(100-digit number)

15146248344178325622…94893144522984847359

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