Block #233,675

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/29/2013, 8:46:22 PM · Difficulty 9.9430 · 6,561,899 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e795a67baf30a25fb7a9cbad23437d5e0758696ab8346e182e7c55e9ea1e85a5

View on Chainz ↗

Height

#233,675

Difficulty

9.943040

Transactions

Size

869 B

Version

Bits

09f16b13

Nonce

29,044

Timestamp

10/29/2013, 8:46:22 PM

Confirmations

6,561,899

Mined by

⛏️ P2SHAefNmfCCiMUgcSMoZqwmWZgc6ARj9JS3UM

Merkle Root

57af417c89997c8a5d1d8d91cf2aa790e7001a1234702ea092438a61ecdbac43

Transactions (2)

Coinbasedabf43337713fe…15d9e6ca308118

1 in → 1 out10.1100 XPM109 B

AefNmfCC…Rj9JS3UM

d89d1a99863a48…aec44c317c6b31

4 in → 2 out25.6777 XPM670 B

Ab8tttyj…sCD7J4AH AXFrXfLw…YhCMkWU9

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.

4.823 × 10⁹⁴(95-digit number)

48235449682101979103…80356950669267286079

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

4.823 × 10⁹⁴(95-digit number)

48235449682101979103…80356950669267286079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.647 × 10⁹⁴(95-digit number)

96470899364203958206…60713901338534572159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.929 × 10⁹⁵(96-digit number)

19294179872840791641…21427802677069144319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.858 × 10⁹⁵(96-digit number)

38588359745681583282…42855605354138288639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.717 × 10⁹⁵(96-digit number)

77176719491363166565…85711210708276577279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.543 × 10⁹⁶(97-digit number)

15435343898272633313…71422421416553154559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.087 × 10⁹⁶(97-digit number)

30870687796545266626…42844842833106309119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.174 × 10⁹⁶(97-digit number)

61741375593090533252…85689685666212618239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.234 × 10⁹⁷(98-digit number)

12348275118618106650…71379371332425236479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.469 × 10⁹⁷(98-digit number)

24696550237236213300…42758742664850472959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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