Block #83,058

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/25/2013, 9:10:43 PM · Difficulty 9.2715 · 6,707,885 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

cbde6d2fca1b58e09740235721e7353f03fcab9e47fe07ed348e9c7a79276d3b

View on Chainz ↗

Height

#83,058

Difficulty

9.271509

Transactions

Size

5.44 KB

Version

Bits

0945819a

Nonce

295,763

Timestamp

7/25/2013, 9:10:43 PM

Confirmations

6,707,885

Merkle Root

92a2a511bd6b2ea045a27dda12402247b40714694f468cda340447522c256cd6

Transactions (3)

Coinbasea9e7b814b4fdde…94ccc35131e969

1 in → 1 out11.6800 XPM109 B

ARrQjqnz…sUp78sSo

14dabeb7f42811…66608483024c11

2 in → 2 out42.8356 XPM374 B

AQRpTqmB…JVzZue3X AKZHGNpJ…FByhphHp

1977dfc9846b6d…9366bfe117b2b1

43 in → 2 out502.7500 XPM4.87 KB

AYRs8Two…pb3Q1Y7S AdNeXXkk…QpfXAns4

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.

2.310 × 10¹⁰⁷(108-digit number)

23109591940185738986…90395364790745807991

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

2.310 × 10¹⁰⁷(108-digit number)

23109591940185738986…90395364790745807991

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.621 × 10¹⁰⁷(108-digit number)

46219183880371477972…80790729581491615981

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.243 × 10¹⁰⁷(108-digit number)

92438367760742955945…61581459162983231961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.848 × 10¹⁰⁸(109-digit number)

18487673552148591189…23162918325966463921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.697 × 10¹⁰⁸(109-digit number)

36975347104297182378…46325836651932927841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.395 × 10¹⁰⁸(109-digit number)

73950694208594364756…92651673303865855681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.479 × 10¹⁰⁹(110-digit number)

14790138841718872951…85303346607731711361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.958 × 10¹⁰⁹(110-digit number)

29580277683437745902…70606693215463422721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.916 × 10¹⁰⁹(110-digit number)

59160555366875491804…41213386430926845441

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer