Block #315,279

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/16/2013, 10:32:23 AM · Difficulty 10.0934 · 6,480,588 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c22bb51a02fdd333b2d30706e175f5e41011c7d042c3f8ade7fdaf660b9d1902

View on Chainz ↗

Height

#315,279

Difficulty

10.093364

Transactions

Size

933 B

Version

Bits

0a17e6b4

Nonce

372,930

Timestamp

12/16/2013, 10:32:23 AM

Confirmations

6,480,588

Mined by

⛏️ aRgAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

fd530ea644aa421d4a5d378bd83be34be037f792d6ced2291452b8d95bc1b329

Transactions (1)

Coinbasefd530ea644aa42…52b8d95bc1b329

1 in → 23 out9.8000 XPM845 B

Aac9Hjdg…P4ktypc3 AJzWx2VD…j4ZSMit5 AL6EFpSH…e9A652s3 AMiJebLB…rK2iN8iS Ad9pSzHt…cpJ3y2zz

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.

6.190 × 10⁸⁹(90-digit number)

61902146302034090401…54055284724465118699

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

6.190 × 10⁸⁹(90-digit number)

61902146302034090401…54055284724465118699

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.238 × 10⁹⁰(91-digit number)

12380429260406818080…08110569448930237399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.476 × 10⁹⁰(91-digit number)

24760858520813636160…16221138897860474799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.952 × 10⁹⁰(91-digit number)

49521717041627272320…32442277795720949599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.904 × 10⁹⁰(91-digit number)

99043434083254544641…64884555591441899199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.980 × 10⁹¹(92-digit number)

19808686816650908928…29769111182883798399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.961 × 10⁹¹(92-digit number)

39617373633301817856…59538222365767596799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.923 × 10⁹¹(92-digit number)

79234747266603635713…19076444731535193599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.584 × 10⁹²(93-digit number)

15846949453320727142…38152889463070387199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.169 × 10⁹²(93-digit number)

31693898906641454285…76305778926140774399

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