Block #454,459

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/21/2014, 10:44:48 PM · Difficulty 10.3994 · 6,355,331 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6aa998a1dcf034839ec4447e09226bcf0ff29ccd6373de3706f54fd241f5f34f

Height

#454,459

Difficulty

10.399411

Transactions

1

Size

1002 B

Version

2

Bits

0a663fce

Nonce

225,122

Timestamp

3/21/2014, 10:44:48 PM

Confirmations

6,355,331

Merkle Root

aedf60ec972d194706cf91090aa10ef77860e9e84d3513cf2a41497db7e6234b
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.

6.117 × 10⁹²(93-digit number)
61176116757827117258…44014153738397140801
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
6.117 × 10⁹²(93-digit number)
61176116757827117258…44014153738397140801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.223 × 10⁹³(94-digit number)
12235223351565423451…88028307476794281601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.447 × 10⁹³(94-digit number)
24470446703130846903…76056614953588563201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.894 × 10⁹³(94-digit number)
48940893406261693806…52113229907177126401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.788 × 10⁹³(94-digit number)
97881786812523387612…04226459814354252801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.957 × 10⁹⁴(95-digit number)
19576357362504677522…08452919628708505601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.915 × 10⁹⁴(95-digit number)
39152714725009355045…16905839257417011201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.830 × 10⁹⁴(95-digit number)
78305429450018710090…33811678514834022401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.566 × 10⁹⁵(96-digit number)
15661085890003742018…67623357029668044801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.132 × 10⁹⁵(96-digit number)
31322171780007484036…35246714059336089601
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:57,722,401 XPM·at block #6,809,789 · updates every 60s
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