Block #1,260,986

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/30/2015, 12:15:34 PM · Difficulty 10.8215 · 5,538,550 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cb0a446224f4833fd3a745dfd917890e81fa1feaae56627c3e6340809a14a1d4

Height

#1,260,986

Difficulty

10.821470

Transactions

4

Size

878 B

Version

2

Bits

0ad24be3

Nonce

818,058,743

Timestamp

9/30/2015, 12:15:34 PM

Confirmations

5,538,550

Merkle Root

f2441056bbd7c2d277bef2a8cbb5b023857a77f164a2bcb4f200eb7290aecaef
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.

6.083 × 10⁹⁴(95-digit number)
60837939129294468600…24273272484004355841
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
6.083 × 10⁹⁴(95-digit number)
60837939129294468600…24273272484004355841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.216 × 10⁹⁵(96-digit number)
12167587825858893720…48546544968008711681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.433 × 10⁹⁵(96-digit number)
24335175651717787440…97093089936017423361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.867 × 10⁹⁵(96-digit number)
48670351303435574880…94186179872034846721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.734 × 10⁹⁵(96-digit number)
97340702606871149760…88372359744069693441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.946 × 10⁹⁶(97-digit number)
19468140521374229952…76744719488139386881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.893 × 10⁹⁶(97-digit number)
38936281042748459904…53489438976278773761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.787 × 10⁹⁶(97-digit number)
77872562085496919808…06978877952557547521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.557 × 10⁹⁷(98-digit number)
15574512417099383961…13957755905115095041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.114 × 10⁹⁷(98-digit number)
31149024834198767923…27915511810230190081
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:57,640,339 XPM·at block #6,799,535 · updates every 60s
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