Block #469,573

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/1/2014, 8:01:44 AM · Difficulty 10.4277 · 6,333,970 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5c1ba00c5a6561fe703f87e5dbe4cf0601a2a6527857a44952fce3cda5df6099

Height

#469,573

Difficulty

10.427663

Transactions

5

Size

1.04 KB

Version

2

Bits

0a6d7b4e

Nonce

861,639

Timestamp

4/1/2014, 8:01:44 AM

Confirmations

6,333,970

Merkle Root

8f041ad383fd2be33adf1a375e8dde5bf18cd53b68899f4e888fcb26a318618a
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.

1.952 × 10⁹⁶(97-digit number)
19528463586328635422…87841520549854281919
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.

1
origin − 1
1.952 × 10⁹⁶(97-digit number)
19528463586328635422…87841520549854281919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.905 × 10⁹⁶(97-digit number)
39056927172657270845…75683041099708563839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.811 × 10⁹⁶(97-digit number)
78113854345314541690…51366082199417127679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.562 × 10⁹⁷(98-digit number)
15622770869062908338…02732164398834255359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.124 × 10⁹⁷(98-digit number)
31245541738125816676…05464328797668510719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.249 × 10⁹⁷(98-digit number)
62491083476251633352…10928657595337021439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.249 × 10⁹⁸(99-digit number)
12498216695250326670…21857315190674042879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.499 × 10⁹⁸(99-digit number)
24996433390500653340…43714630381348085759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.999 × 10⁹⁸(99-digit number)
49992866781001306681…87429260762696171519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.998 × 10⁹⁸(99-digit number)
99985733562002613363…74858521525392343039
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, …
Circulating Supply:57,672,374 XPM·at block #6,803,542 · updates every 60s
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