Block #462,720

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/27/2014, 3:10:16 PM · Difficulty 10.4147 · 6,346,440 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
622f93d35b6b2c41b974113bb5105abdf5137bb7a96c6ac4d47106c77c20b0f5

Height

#462,720

Difficulty

10.414654

Transactions

4

Size

47.94 KB

Version

2

Bits

0a6a26c8

Nonce

2,094,870,847

Timestamp

3/27/2014, 3:10:16 PM

Confirmations

6,346,440

Merkle Root

9336ff09701e86ec43d92679c040d4d5f0b73aaea612d39f6f0977a535b4df79
Transactions (4)
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.

2.124 × 10⁹⁴(95-digit number)
21244641035638597004…63729878921993756569
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
2.124 × 10⁹⁴(95-digit number)
21244641035638597004…63729878921993756569
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.248 × 10⁹⁴(95-digit number)
42489282071277194008…27459757843987513139
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.497 × 10⁹⁴(95-digit number)
84978564142554388016…54919515687975026279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.699 × 10⁹⁵(96-digit number)
16995712828510877603…09839031375950052559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.399 × 10⁹⁵(96-digit number)
33991425657021755206…19678062751900105119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.798 × 10⁹⁵(96-digit number)
67982851314043510413…39356125503800210239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.359 × 10⁹⁶(97-digit number)
13596570262808702082…78712251007600420479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.719 × 10⁹⁶(97-digit number)
27193140525617404165…57424502015200840959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.438 × 10⁹⁶(97-digit number)
54386281051234808330…14849004030401681919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.087 × 10⁹⁷(98-digit number)
10877256210246961666…29698008060803363839
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:57,717,341 XPM·at block #6,809,159 · updates every 60s
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