Block #102,470

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/7/2013, 3:40:23 AM · Difficulty 9.4946 · 6,722,964 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

acd339633c8a8c08833f8e2a2d197247fa792f20ebb534a2c4b653f482ade3ab

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Height

#102,470

Difficulty

9.494556

Transactions

Size

1.62 KB

Version

Bits

097e9b33

Nonce

3,234

Timestamp

8/7/2013, 3:40:23 AM

Confirmations

6,722,964

Mined by

⛏️ P2SHAHHQevHnq2jjHsw5wvhgvvxs2ZZDrhzQHJ

Merkle Root

c94d3477e038f80384d417978d25aac1bf51f046dbae056b1e8a7c343f1232d0

Transactions (3)

Coinbase2d416922e1aa40…4f02246cb32eab

1 in → 1 out11.1008 XPM110 B

AHHQevHn…ZDrhzQHJ

593a44d697d85c…1722dbb7ef8574

4 in → 1 out94.5390 XPM636 B

AKiocCsS…cCeJbdAv

8600a30e3ae589…a6b8ccc6bbce9f

5 in → 2 out7.2450 XPM817 B

AVMgfoke…qsxnTzjM AWeWcPM1…BA2a8s16

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.

1.606 × 10⁹⁷(98-digit number)

16065018361885181124…12233594019267227599

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

1.606 × 10⁹⁷(98-digit number)

16065018361885181124…12233594019267227599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.213 × 10⁹⁷(98-digit number)

32130036723770362249…24467188038534455199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.426 × 10⁹⁷(98-digit number)

64260073447540724499…48934376077068910399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.285 × 10⁹⁸(99-digit number)

12852014689508144899…97868752154137820799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.570 × 10⁹⁸(99-digit number)

25704029379016289799…95737504308275641599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.140 × 10⁹⁸(99-digit number)

51408058758032579599…91475008616551283199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.028 × 10⁹⁹(100-digit number)

10281611751606515919…82950017233102566399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.056 × 10⁹⁹(100-digit number)

20563223503213031839…65900034466205132799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.112 × 10⁹⁹(100-digit number)

41126447006426063679…31800068932410265599

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 #102,470

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