Block #609,875

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/1/2014, 10:46:08 AM · Difficulty 10.9140 · 6,186,074 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6463dc1ac97296f77e879da17b1a54b5293e5cc159e27411c18720a73817b111

View on Chainz ↗

Height

#609,875

Difficulty

10.914005

Transactions

Size

580 B

Version

Bits

0ae9fc3b

Nonce

482,872,868

Timestamp

7/1/2014, 10:46:08 AM

Confirmations

6,186,074

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9b187b4edca41d2b5f180c4608ec2e5046073e195387d5caabdfb025f06a2f62

Transactions (2)

Coinbase207dd00d706cad…0a41099b417aab

1 in → 1 out8.3900 XPM116 B

ANSXnLY2…Sd25TjkD

1fa23dfcc5a47a…2a624f85cbaf84

2 in → 2 out1.0653 XPM373 B

Abns1anC…CZnwCT9h AakdFfvF…nsCVqJob

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.

2.607 × 10⁹⁶(97-digit number)

26071092747697047496…09188523091191306239

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

2.607 × 10⁹⁶(97-digit number)

26071092747697047496…09188523091191306239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.214 × 10⁹⁶(97-digit number)

52142185495394094993…18377046182382612479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.042 × 10⁹⁷(98-digit number)

10428437099078818998…36754092364765224959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.085 × 10⁹⁷(98-digit number)

20856874198157637997…73508184729530449919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.171 × 10⁹⁷(98-digit number)

41713748396315275995…47016369459060899839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.342 × 10⁹⁷(98-digit number)

83427496792630551990…94032738918121799679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.668 × 10⁹⁸(99-digit number)

16685499358526110398…88065477836243599359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.337 × 10⁹⁸(99-digit number)

33370998717052220796…76130955672487198719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.674 × 10⁹⁸(99-digit number)

66741997434104441592…52261911344974397439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.334 × 10⁹⁹(100-digit number)

13348399486820888318…04523822689948794879

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