Block #1,606,792

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/30/2016, 2:36:25 PM · Difficulty 10.6080 · 5,224,878 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
246870953dc8bc77c09d564c06c2dd9f4f88601f732b24975856c40b73c4a2af

Height

#1,606,792

Difficulty

10.608034

Transactions

2

Size

1.43 KB

Version

2

Bits

0a9ba817

Nonce

290,299,388

Timestamp

5/30/2016, 2:36:25 PM

Confirmations

5,224,878

Merkle Root

c13c10897163ebf712d00996401a6981ca2a7d9f548770e2378a06da66fa10dd
Transactions (2)
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.

4.828 × 10⁹¹(92-digit number)
48287506645164160799…50902094881968316321
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
4.828 × 10⁹¹(92-digit number)
48287506645164160799…50902094881968316321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.657 × 10⁹¹(92-digit number)
96575013290328321599…01804189763936632641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.931 × 10⁹²(93-digit number)
19315002658065664319…03608379527873265281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.863 × 10⁹²(93-digit number)
38630005316131328639…07216759055746530561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.726 × 10⁹²(93-digit number)
77260010632262657279…14433518111493061121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.545 × 10⁹³(94-digit number)
15452002126452531455…28867036222986122241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.090 × 10⁹³(94-digit number)
30904004252905062911…57734072445972244481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.180 × 10⁹³(94-digit number)
61808008505810125823…15468144891944488961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.236 × 10⁹⁴(95-digit number)
12361601701162025164…30936289783888977921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.472 × 10⁹⁴(95-digit number)
24723203402324050329…61872579567777955841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.944 × 10⁹⁴(95-digit number)
49446406804648100658…23745159135555911681
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,897,465 XPM·at block #6,831,669 · updates every 60s
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