Block #672,680

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 8/11/2014, 2:05:35 AM · Difficulty 10.9649 · 6,137,662 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ce15de2fc76e79c5cf2675cc705a7ed16584ff71b55ec2c4bbd4b82f141dbf08

Height

#672,680

Difficulty

10.964884

Transactions

2

Size

433 B

Version

2

Bits

0af702a0

Nonce

812,517,583

Timestamp

8/11/2014, 2:05:35 AM

Confirmations

6,137,662

Merkle Root

4010b0d058dd361fd2f1002c65ccc52e755c0d368e6bb97e4a9b04ca52191339
Transactions (2)
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.

2.190 × 10⁹⁵(96-digit number)
21905423523880683752…45550956762884788151
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
2.190 × 10⁹⁵(96-digit number)
21905423523880683752…45550956762884788151
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.381 × 10⁹⁵(96-digit number)
43810847047761367505…91101913525769576301
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.762 × 10⁹⁵(96-digit number)
87621694095522735011…82203827051539152601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.752 × 10⁹⁶(97-digit number)
17524338819104547002…64407654103078305201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.504 × 10⁹⁶(97-digit number)
35048677638209094004…28815308206156610401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.009 × 10⁹⁶(97-digit number)
70097355276418188008…57630616412313220801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.401 × 10⁹⁷(98-digit number)
14019471055283637601…15261232824626441601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.803 × 10⁹⁷(98-digit number)
28038942110567275203…30522465649252883201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.607 × 10⁹⁷(98-digit number)
56077884221134550407…61044931298505766401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.121 × 10⁹⁸(99-digit number)
11215576844226910081…22089862597011532801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.243 × 10⁹⁸(99-digit number)
22431153688453820162…44179725194023065601
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:57,726,818 XPM·at block #6,810,341 · updates every 60s
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