Block #1,605,048

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/29/2016, 11:04:23 AM · Difficulty 10.6009 · 5,211,498 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
16d086eb0adb692be2c84582e04fcb9cb3253b7babb25901e1860983acb1fd3f

Height

#1,605,048

Difficulty

10.600912

Transactions

2

Size

970 B

Version

2

Bits

0a99d55a

Nonce

490,315,109

Timestamp

5/29/2016, 11:04:23 AM

Confirmations

5,211,498

Merkle Root

d6dbdf4259f6152b736e08f378da1d614bb40acab4c5aad22ff65fce6ede326f
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.

9.196 × 10⁹⁴(95-digit number)
91966759700452122892…15944530065549503679
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
9.196 × 10⁹⁴(95-digit number)
91966759700452122892…15944530065549503679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.839 × 10⁹⁵(96-digit number)
18393351940090424578…31889060131099007359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.678 × 10⁹⁵(96-digit number)
36786703880180849156…63778120262198014719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.357 × 10⁹⁵(96-digit number)
73573407760361698313…27556240524396029439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.471 × 10⁹⁶(97-digit number)
14714681552072339662…55112481048792058879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.942 × 10⁹⁶(97-digit number)
29429363104144679325…10224962097584117759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.885 × 10⁹⁶(97-digit number)
58858726208289358650…20449924195168235519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.177 × 10⁹⁷(98-digit number)
11771745241657871730…40899848390336471039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.354 × 10⁹⁷(98-digit number)
23543490483315743460…81799696780672942079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.708 × 10⁹⁷(98-digit number)
47086980966631486920…63599393561345884159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
9.417 × 10⁹⁷(98-digit number)
94173961933262973841…27198787122691768319
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,776,497 XPM·at block #6,816,545 · updates every 60s
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