Block #365,086

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/18/2014, 12:25:00 PM · Difficulty 10.4235 · 6,437,527 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7cf52cb66f52f8789b93eab932f72920842d390d31e969ea1d0b532c16799bd8

View on Chainz ↗

Height

#365,086

Difficulty

10.423537

Transactions

Size

230 B

Version

Bits

0a6c6ce9

Nonce

9,707

Timestamp

1/18/2014, 12:25:00 PM

Confirmations

6,437,527

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

720f6f38fd05fdfa8b5e3d4e9c225a09f2a1ca6d042b2ff8500a36e5fe96a4b1

Transactions (1)

Coinbase720f6f38fd05fd…0a36e5fe96a4b1

1 in → 2 out9.1900 XPM137 B

ARmAMwyu…P7Kn74ZT AHsw4d6U…EnM8UXNZ

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.

2.963 × 10¹⁰²(103-digit number)

29635574606712154796…89305777951801396959

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

2.963 × 10¹⁰²(103-digit number)

29635574606712154796…89305777951801396959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.927 × 10¹⁰²(103-digit number)

59271149213424309592…78611555903602793919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.185 × 10¹⁰³(104-digit number)

11854229842684861918…57223111807205587839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.370 × 10¹⁰³(104-digit number)

23708459685369723836…14446223614411175679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.741 × 10¹⁰³(104-digit number)

47416919370739447673…28892447228822351359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.483 × 10¹⁰³(104-digit number)

94833838741478895347…57784894457644702719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.896 × 10¹⁰⁴(105-digit number)

18966767748295779069…15569788915289405439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.793 × 10¹⁰⁴(105-digit number)

37933535496591558138…31139577830578810879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.586 × 10¹⁰⁴(105-digit number)

75867070993183116277…62279155661157621759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.517 × 10¹⁰⁵(106-digit number)

15173414198636623255…24558311322315243519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

3.034 × 10¹⁰⁵(106-digit number)

30346828397273246511…49116622644630487039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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