Block #2,920,373

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/12/2018, 7:35:37 PM · Difficulty 11.3919 · 3,922,018 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
691b507cd8205a1181f2367eb99cd6b1bee69add9c12a41f4c0420409d52771b

Height

#2,920,373

Difficulty

11.391880

Transactions

4

Size

1.29 KB

Version

2

Bits

0b645247

Nonce

810,005,078

Timestamp

11/12/2018, 7:35:37 PM

Confirmations

3,922,018

Merkle Root

2a855b1ccf3de41de1f758376bf4fa48311befbea77601207c4f5098b0f3e65f
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.

7.605 × 10⁹⁵(96-digit number)
76058857674771653481…84014394400068008959
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
7.605 × 10⁹⁵(96-digit number)
76058857674771653481…84014394400068008959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.521 × 10⁹⁶(97-digit number)
15211771534954330696…68028788800136017919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.042 × 10⁹⁶(97-digit number)
30423543069908661392…36057577600272035839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.084 × 10⁹⁶(97-digit number)
60847086139817322785…72115155200544071679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.216 × 10⁹⁷(98-digit number)
12169417227963464557…44230310401088143359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.433 × 10⁹⁷(98-digit number)
24338834455926929114…88460620802176286719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.867 × 10⁹⁷(98-digit number)
48677668911853858228…76921241604352573439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.735 × 10⁹⁷(98-digit number)
97355337823707716456…53842483208705146879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.947 × 10⁹⁸(99-digit number)
19471067564741543291…07684966417410293759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.894 × 10⁹⁸(99-digit number)
38942135129483086582…15369932834820587519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.788 × 10⁹⁸(99-digit number)
77884270258966173164…30739865669641175039
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:57,983,538 XPM·at block #6,842,390 · updates every 60s
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