Block #485,372

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 12:41:17 AM · Difficulty 10.6077 · 6,339,658 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
74665b3c27e1289f33aa25c99ab07824b03ea06e1094ec3a65ab8aaa161c73a4

Height

#485,372

Difficulty

10.607701

Transactions

4

Size

1.44 KB

Version

2

Bits

0a9b924f

Nonce

62,294

Timestamp

4/11/2014, 12:41:17 AM

Confirmations

6,339,658

Merkle Root

1e1d3875df989c9b0da8c3bdd7c32e3718bc390daeb069ac13c260e460ee4b4a
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.

1.150 × 10¹⁰⁶(107-digit number)
11505404279680777015…18279053558243186161
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
1.150 × 10¹⁰⁶(107-digit number)
11505404279680777015…18279053558243186161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.301 × 10¹⁰⁶(107-digit number)
23010808559361554030…36558107116486372321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.602 × 10¹⁰⁶(107-digit number)
46021617118723108060…73116214232972744641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.204 × 10¹⁰⁶(107-digit number)
92043234237446216120…46232428465945489281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.840 × 10¹⁰⁷(108-digit number)
18408646847489243224…92464856931890978561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.681 × 10¹⁰⁷(108-digit number)
36817293694978486448…84929713863781957121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.363 × 10¹⁰⁷(108-digit number)
73634587389956972896…69859427727563914241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.472 × 10¹⁰⁸(109-digit number)
14726917477991394579…39718855455127828481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.945 × 10¹⁰⁸(109-digit number)
29453834955982789158…79437710910255656961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.890 × 10¹⁰⁸(109-digit number)
58907669911965578317…58875421820511313921
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,844,323 XPM·at block #6,825,029 · updates every 60s
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