Block #574,812

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/3/2014, 1:50:16 PM · Difficulty 10.9679 · 6,236,341 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bb70aafaac59d1f22e6927db31880700dca3da0fecd304d4cf730c36b653556d

View on Chainz ↗

Height

#574,812

Difficulty

10.967905

Transactions

Size

562 B

Version

Bits

0af7c89b

Nonce

53,312

Timestamp

6/3/2014, 1:50:16 PM

Confirmations

6,236,341

Mined by

⛏️ \aS?AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9a8cf7e2bed31de27b113c125b06a0901a6fe3cdee77efab05f88bcce7ac3d0d

Transactions (1)

Coinbase9a8cf7e2bed31d…f88bcce7ac3d0d

1 in → 12 out8.2977 XPM471 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AdxPNkWD…ZMa9u34q AQyr8Lw3…hs4nt3Pn

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.

1.162 × 10⁹⁷(98-digit number)

11624519716618821130…67013125160944261119

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

1.162 × 10⁹⁷(98-digit number)

11624519716618821130…67013125160944261119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.324 × 10⁹⁷(98-digit number)

23249039433237642261…34026250321888522239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.649 × 10⁹⁷(98-digit number)

46498078866475284523…68052500643777044479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.299 × 10⁹⁷(98-digit number)

92996157732950569046…36105001287554088959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.859 × 10⁹⁸(99-digit number)

18599231546590113809…72210002575108177919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.719 × 10⁹⁸(99-digit number)

37198463093180227618…44420005150216355839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.439 × 10⁹⁸(99-digit number)

74396926186360455237…88840010300432711679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.487 × 10⁹⁹(100-digit number)

14879385237272091047…77680020600865423359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.975 × 10⁹⁹(100-digit number)

29758770474544182094…55360041201730846719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.951 × 10⁹⁹(100-digit number)

59517540949088364189…10720082403461693439

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 #574,812

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