Block #170,278

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/18/2013, 3:57:44 PM · Difficulty 9.8656 · 6,657,031 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c2237978f5495721dba8074dea3824611ef3fa9315561ffb448bbd4d22fcb36e

View on Chainz ↗

Height

#170,278

Difficulty

9.865565

Transactions

Size

573 B

Version

Bits

09dd95a4

Nonce

3,581

Timestamp

9/18/2013, 3:57:44 PM

Confirmations

6,657,031

Mined by

⛏️ P2SHAYAQXZPvQaoA6c4aUKZj3RaDPJKmQLMRtW

Merkle Root

08572f1b265f479ce16bc7befb1cbef9d7fc6ab2172afbcfd86121bd6308d62b

Transactions (2)

Coinbase02bbb5b5ba5180…cfe256bad5db72

1 in → 1 out10.2700 XPM109 B

AYAQXZPv…KmQLMRtW

4bacfde478422e…ab3d7683f47a01

2 in → 2 out2.2918 XPM373 B

AUTkHTPW…eo8qy2df AMDv5pyi…oUbc4K5x

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.

6.347 × 10⁹⁷(98-digit number)

63476198433725743652…36184782375617879999

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

6.347 × 10⁹⁷(98-digit number)

63476198433725743652…36184782375617879999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.269 × 10⁹⁸(99-digit number)

12695239686745148730…72369564751235759999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.539 × 10⁹⁸(99-digit number)

25390479373490297461…44739129502471519999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.078 × 10⁹⁸(99-digit number)

50780958746980594922…89478259004943039999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.015 × 10⁹⁹(100-digit number)

10156191749396118984…78956518009886079999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.031 × 10⁹⁹(100-digit number)

20312383498792237968…57913036019772159999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.062 × 10⁹⁹(100-digit number)

40624766997584475937…15826072039544319999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.124 × 10⁹⁹(100-digit number)

81249533995168951875…31652144079088639999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.624 × 10¹⁰⁰(101-digit number)

16249906799033790375…63304288158177279999

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 #170,278

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