Block #365,594

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2014, 9:00:36 PM · Difficulty 10.4235 · 6,439,467 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d7d5044ca1e116aa0748907cb4985bd5652d902b1bd91d94d193a03e501a3d5b

Height

#365,594

Difficulty

10.423483

Transactions

4

Size

886 B

Version

2

Bits

0a6c695c

Nonce

666,978

Timestamp

1/18/2014, 9:00:36 PM

Confirmations

6,439,467

Merkle Root

a0e0c9a041403cc64d79caf1c1cec2d9348fe4e7db8c3917945c0c5bf0fbce11
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.

1.579 × 10⁹⁹(100-digit number)
15794648075219336441…68978972539477372161
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
1.579 × 10⁹⁹(100-digit number)
15794648075219336441…68978972539477372161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.158 × 10⁹⁹(100-digit number)
31589296150438672883…37957945078954744321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.317 × 10⁹⁹(100-digit number)
63178592300877345767…75915890157909488641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.263 × 10¹⁰⁰(101-digit number)
12635718460175469153…51831780315818977281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.527 × 10¹⁰⁰(101-digit number)
25271436920350938306…03663560631637954561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.054 × 10¹⁰⁰(101-digit number)
50542873840701876613…07327121263275909121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.010 × 10¹⁰¹(102-digit number)
10108574768140375322…14654242526551818241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.021 × 10¹⁰¹(102-digit number)
20217149536280750645…29308485053103636481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.043 × 10¹⁰¹(102-digit number)
40434299072561501291…58616970106207272961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.086 × 10¹⁰¹(102-digit number)
80868598145123002582…17233940212414545921
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:57,684,554 XPM·at block #6,805,060 · updates every 60s
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