Block #484,078

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 9:15:54 AM · Difficulty 10.5778 · 6,324,560 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a0bf661790ff548de3e1b8352847bbbd5bcf7bacfedbbfe18fb16b4ca9d299fc

Height

#484,078

Difficulty

10.577784

Transactions

2

Size

860 B

Version

2

Bits

0a93e9a0

Nonce

134,225,297

Timestamp

4/10/2014, 9:15:54 AM

Confirmations

6,324,560

Merkle Root

e2eb2472815ef23d0ba365147f7a0ef940b0edafa90799a58f49167042f8c3e0
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.

1.486 × 10⁹⁵(96-digit number)
14860752779722927922…84012731534203843001
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
1.486 × 10⁹⁵(96-digit number)
14860752779722927922…84012731534203843001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.972 × 10⁹⁵(96-digit number)
29721505559445855845…68025463068407686001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.944 × 10⁹⁵(96-digit number)
59443011118891711691…36050926136815372001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.188 × 10⁹⁶(97-digit number)
11888602223778342338…72101852273630744001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.377 × 10⁹⁶(97-digit number)
23777204447556684676…44203704547261488001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.755 × 10⁹⁶(97-digit number)
47554408895113369353…88407409094522976001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.510 × 10⁹⁶(97-digit number)
95108817790226738706…76814818189045952001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.902 × 10⁹⁷(98-digit number)
19021763558045347741…53629636378091904001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.804 × 10⁹⁷(98-digit number)
38043527116090695482…07259272756183808001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.608 × 10⁹⁷(98-digit number)
76087054232181390965…14518545512367616001
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:57,713,155 XPM·at block #6,808,637 · updates every 60s
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