Block #70,220

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 12:33:17 PM · Difficulty 8.9919 · 6,722,630 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

80762109afbb16d937b9c3cdd6e0ce0b78175a1289a10f2e66e20a93bd96f18b

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Height

#70,220

Difficulty

8.991900

Transactions

Size

11.07 KB

Version

Bits

08fded22

Nonce

874

Timestamp

7/20/2013, 12:33:17 PM

Confirmations

6,722,630

Merkle Root

92d1e0a36f53ab3a68f3af4b8a587bbd22acf5e60309de0d5ee46db7583ec55d

Transactions (2)

Coinbaseddcfc4194d3517…f275aab2534e03

1 in → 1 out12.4700 XPM110 B

AP8WMgEZ…hNhLjYfp

bc499964f878eb…80c7968c6918e7

97 in → 2 out1206.8900 XPM10.88 KB

ARsrDwcp…Fv5SKr8Y AWT4yJH9…s3xK7KZ3

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.

1.075 × 10⁹⁵(96-digit number)

10753938299266628318…80657709039024241921

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

1.075 × 10⁹⁵(96-digit number)

10753938299266628318…80657709039024241921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.150 × 10⁹⁵(96-digit number)

21507876598533256637…61315418078048483841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.301 × 10⁹⁵(96-digit number)

43015753197066513274…22630836156096967681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.603 × 10⁹⁵(96-digit number)

86031506394133026549…45261672312193935361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.720 × 10⁹⁶(97-digit number)

17206301278826605309…90523344624387870721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.441 × 10⁹⁶(97-digit number)

34412602557653210619…81046689248775741441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.882 × 10⁹⁶(97-digit number)

68825205115306421239…62093378497551482881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.376 × 10⁹⁷(98-digit number)

13765041023061284247…24186756995102965761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.753 × 10⁹⁷(98-digit number)

27530082046122568495…48373513990205931521

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