Block #114,856

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/13/2013, 10:12:31 AM · Difficulty 9.7408 · 6,694,906 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fc484cbc29e2ebb73b9b803bd281a0d97e15ab43ab28d260a5f215a020ae0bd9

View on Chainz ↗

Height

#114,856

Difficulty

9.740756

Transactions

Size

511 B

Version

Bits

09bda235

Nonce

126,196

Timestamp

8/13/2013, 10:12:31 AM

Confirmations

6,694,906

Mined by

⛏️ P2SHANjcSq7EJEvXSiR3fYrCvonHsctSZur1ho

Merkle Root

0ed9561ffc1d33abc5a9a0c108e79bf202d02209020fe825d7327f0226ea9ae4

Transactions (2)

Coinbase2b581715defe48…19be426c5b5ed7

1 in → 1 out10.5300 XPM109 B

ANjcSq7E…tSZur1ho

bd845d1ab7f062…da80fe7ad9e794

2 in → 1 out11.4100 XPM308 B

AZiCNyEn…BjhGoBch

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.

1.399 × 10¹⁰³(104-digit number)

13992481880862824824…04138998765319803049

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

1.399 × 10¹⁰³(104-digit number)

13992481880862824824…04138998765319803049

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.798 × 10¹⁰³(104-digit number)

27984963761725649648…08277997530639606099

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.596 × 10¹⁰³(104-digit number)

55969927523451299297…16555995061279212199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.119 × 10¹⁰⁴(105-digit number)

11193985504690259859…33111990122558424399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.238 × 10¹⁰⁴(105-digit number)

22387971009380519719…66223980245116848799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.477 × 10¹⁰⁴(105-digit number)

44775942018761039438…32447960490233697599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.955 × 10¹⁰⁴(105-digit number)

89551884037522078876…64895920980467395199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.791 × 10¹⁰⁵(106-digit number)

17910376807504415775…29791841960934790399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.582 × 10¹⁰⁵(106-digit number)

35820753615008831550…59583683921869580799

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 #114,856

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