Block #113,707

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/12/2013, 4:52:48 PM · Difficulty 9.7350 · 6,713,455 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6f7dde61e41f52c25820f54a06df97f5b4a60b43b6a062663164be22767b7d9c

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Height

#113,707

Difficulty

9.734972

Transactions

Size

202 B

Version

Bits

09bc271c

Nonce

203,824

Timestamp

8/12/2013, 4:52:48 PM

Confirmations

6,713,455

Mined by

⛏️ P2SHAMYUL1XY1HPqSCSMa5ah7SRkgVt3WZL89n

Merkle Root

22dbc9273e69d16023620b347d6ad7634ea9793928dbb610838484a0afc8984d

Transactions (1)

Coinbase22dbc9273e69d1…8484a0afc8984d

1 in → 1 out10.5400 XPM109 B

AMYUL1XY…t3WZL89n

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.

6.876 × 10¹⁰¹(102-digit number)

68761433775207765187…68149970842926560059

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

6.876 × 10¹⁰¹(102-digit number)

68761433775207765187…68149970842926560059

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.375 × 10¹⁰²(103-digit number)

13752286755041553037…36299941685853120119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.750 × 10¹⁰²(103-digit number)

27504573510083106075…72599883371706240239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.500 × 10¹⁰²(103-digit number)

55009147020166212150…45199766743412480479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.100 × 10¹⁰³(104-digit number)

11001829404033242430…90399533486824960959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.200 × 10¹⁰³(104-digit number)

22003658808066484860…80799066973649921919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.400 × 10¹⁰³(104-digit number)

44007317616132969720…61598133947299843839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.801 × 10¹⁰³(104-digit number)

88014635232265939440…23196267894599687679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.760 × 10¹⁰⁴(105-digit number)

17602927046453187888…46392535789199375359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #113,707

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