Block #1,264,306

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/2/2015, 7:03:44 PM · Difficulty 10.8227 · 5,579,222 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bb12c0e6d457fbe2fc2668c43dcdeadc53fae094a3931e88f7d4c78f212b646

Height

#1,264,306

Difficulty

10.822698

Transactions

2

Size

1.02 KB

Version

2

Bits

0ad29c52

Nonce

810,046,492

Timestamp

10/2/2015, 7:03:44 PM

Confirmations

5,579,222

Merkle Root

40494846e12b451ff21bea257ff27be1f0397d91e070088cd8efc60b741d98a9
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.

9.570 × 10⁹⁵(96-digit number)
95704003436265866570…75478708021857622721
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
9.570 × 10⁹⁵(96-digit number)
95704003436265866570…75478708021857622721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.914 × 10⁹⁶(97-digit number)
19140800687253173314…50957416043715245441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.828 × 10⁹⁶(97-digit number)
38281601374506346628…01914832087430490881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.656 × 10⁹⁶(97-digit number)
76563202749012693256…03829664174860981761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.531 × 10⁹⁷(98-digit number)
15312640549802538651…07659328349721963521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.062 × 10⁹⁷(98-digit number)
30625281099605077302…15318656699443927041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.125 × 10⁹⁷(98-digit number)
61250562199210154605…30637313398887854081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.225 × 10⁹⁸(99-digit number)
12250112439842030921…61274626797775708161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.450 × 10⁹⁸(99-digit number)
24500224879684061842…22549253595551416321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.900 × 10⁹⁸(99-digit number)
49000449759368123684…45098507191102832641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
9.800 × 10⁹⁸(99-digit number)
98000899518736247368…90197014382205665281
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,992,601 XPM·at block #6,843,527 · updates every 60s
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