Block #1,221,476

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/4/2015, 8:26:25 AM · Difficulty 10.7414 · 5,586,656 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
487784eca9539d01b5d35566dfe9101a13ebe288cc1e0c4d9bb2ac90b494ff0e

Height

#1,221,476

Difficulty

10.741395

Transactions

5

Size

5.96 KB

Version

2

Bits

0abdcc17

Nonce

1,453,679,287

Timestamp

9/4/2015, 8:26:25 AM

Confirmations

5,586,656

Merkle Root

ec18854b6ff7a44822555dad17639f1e0c3fa4f01c6a2f13a94c7d4f70f9cc8c
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.

3.580 × 10⁹³(94-digit number)
35809408182319163198…60127107818555524401
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
3.580 × 10⁹³(94-digit number)
35809408182319163198…60127107818555524401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.161 × 10⁹³(94-digit number)
71618816364638326396…20254215637111048801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.432 × 10⁹⁴(95-digit number)
14323763272927665279…40508431274222097601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.864 × 10⁹⁴(95-digit number)
28647526545855330558…81016862548444195201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.729 × 10⁹⁴(95-digit number)
57295053091710661116…62033725096888390401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.145 × 10⁹⁵(96-digit number)
11459010618342132223…24067450193776780801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.291 × 10⁹⁵(96-digit number)
22918021236684264446…48134900387553561601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.583 × 10⁹⁵(96-digit number)
45836042473368528893…96269800775107123201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.167 × 10⁹⁵(96-digit number)
91672084946737057786…92539601550214246401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.833 × 10⁹⁶(97-digit number)
18334416989347411557…85079203100428492801
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:57,709,097 XPM·at block #6,808,131 · updates every 60s
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