Block #1,901,321

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 12/19/2016, 6:14:16 AM · Difficulty 10.7803 · 4,924,103 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
23814f1884e7c970d6f1bbd1b47e8154af7e474e6208947e16b68b692c5e7218

Height

#1,901,321

Difficulty

10.780285

Transactions

2

Size

981 B

Version

2

Bits

0ac7c0ca

Nonce

965,010,558

Timestamp

12/19/2016, 6:14:16 AM

Confirmations

4,924,103

Merkle Root

aa35ad28600b1ba04e4abbde0740abfce181a337841f3be48db06edb148a1cb9
Transactions (2)
1 in → 1 out8.6000 XPM109 B
5 in → 1 out1414.9950 XPM782 B
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.

2.112 × 10⁹⁵(96-digit number)
21124675260090579772…60647225925511983999
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
2.112 × 10⁹⁵(96-digit number)
21124675260090579772…60647225925511983999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.224 × 10⁹⁵(96-digit number)
42249350520181159545…21294451851023967999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.449 × 10⁹⁵(96-digit number)
84498701040362319091…42588903702047935999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.689 × 10⁹⁶(97-digit number)
16899740208072463818…85177807404095871999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.379 × 10⁹⁶(97-digit number)
33799480416144927636…70355614808191743999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.759 × 10⁹⁶(97-digit number)
67598960832289855273…40711229616383487999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.351 × 10⁹⁷(98-digit number)
13519792166457971054…81422459232766975999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.703 × 10⁹⁷(98-digit number)
27039584332915942109…62844918465533951999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.407 × 10⁹⁷(98-digit number)
54079168665831884218…25689836931067903999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.081 × 10⁹⁸(99-digit number)
10815833733166376843…51379673862135807999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.163 × 10⁹⁸(99-digit number)
21631667466332753687…02759347724271615999
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:57,847,493 XPM·at block #6,825,423 · updates every 60s
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