Block #131,172

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/24/2013, 2:02:45 AM · Difficulty 9.7868 · 6,661,295 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

747cb8c837efd0366587b01149319bb2e9f41216db7a63d7cecfe9e7c8257506

View on Chainz ↗

Height

#131,172

Difficulty

9.786755

Transactions

Size

541 B

Version

Bits

09c968c2

Nonce

617,144

Timestamp

8/24/2013, 2:02:45 AM

Confirmations

6,661,295

Merkle Root

7f0b737cf3a3bfc2bf6f829554816e21cbd4d44c81fc070b29873b5806a4d954

Transactions (2)

Coinbaseb23072c2bd1b98…1352be416346c0

1 in → 1 out10.4400 XPM109 B

AdeKMF9w…rSNk3pYm

cb5528eb4daae7…ed849c99a896ba

2 in → 1 out392.2400 XPM340 B

ATDg1wpK…dc5kwZ3e

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.

1.238 × 10⁹⁹(100-digit number)

12382959983500359071…59519402127256436479

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

1.238 × 10⁹⁹(100-digit number)

12382959983500359071…59519402127256436479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.476 × 10⁹⁹(100-digit number)

24765919967000718143…19038804254512872959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.953 × 10⁹⁹(100-digit number)

49531839934001436286…38077608509025745919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.906 × 10⁹⁹(100-digit number)

99063679868002872573…76155217018051491839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.981 × 10¹⁰⁰(101-digit number)

19812735973600574514…52310434036102983679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.962 × 10¹⁰⁰(101-digit number)

39625471947201149029…04620868072205967359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.925 × 10¹⁰⁰(101-digit number)

79250943894402298058…09241736144411934719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.585 × 10¹⁰¹(102-digit number)

15850188778880459611…18483472288823869439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.170 × 10¹⁰¹(102-digit number)

31700377557760919223…36966944577647738879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.340 × 10¹⁰¹(102-digit number)

63400755115521838447…73933889155295477759

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