Block #455,865

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/22/2014, 7:55:19 PM · Difficulty 10.4170 · 6,360,479 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8beae5dc874bbb675c54b55da7f13074a001eb3537cc3451d93bc9b366067ade

Height

#455,865

Difficulty

10.416974

Transactions

1

Size

1003 B

Version

2

Bits

0a6abed5

Nonce

165,997

Timestamp

3/22/2014, 7:55:19 PM

Confirmations

6,360,479

Merkle Root

92c25f905fd15c0cad35e1127083258532578b7d76182164b3bca980c09efc6c
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.

1.087 × 10⁹⁵(96-digit number)
10872415852441349226…49081155062160379241
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
1.087 × 10⁹⁵(96-digit number)
10872415852441349226…49081155062160379241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.174 × 10⁹⁵(96-digit number)
21744831704882698453…98162310124320758481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.348 × 10⁹⁵(96-digit number)
43489663409765396906…96324620248641516961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.697 × 10⁹⁵(96-digit number)
86979326819530793813…92649240497283033921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.739 × 10⁹⁶(97-digit number)
17395865363906158762…85298480994566067841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.479 × 10⁹⁶(97-digit number)
34791730727812317525…70596961989132135681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.958 × 10⁹⁶(97-digit number)
69583461455624635050…41193923978264271361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.391 × 10⁹⁷(98-digit number)
13916692291124927010…82387847956528542721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.783 × 10⁹⁷(98-digit number)
27833384582249854020…64775695913057085441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.566 × 10⁹⁷(98-digit number)
55666769164499708040…29551391826114170881
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:57,774,876 XPM·at block #6,816,343 · updates every 60s
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