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Block #1,318,368

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/8/2015, 11:15:26 AM Β· Difficulty 10.8632 Β· 5,498,816 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3df47b9cf505e8c5f058568c800d15116a10f6f1986630c092777b4b43ff514b
View on Chainz β†—

Height

#1,318,368

Difficulty

10.863212

Transactions

2

Size

4.47 KB

Version

2

Bits

0adcfb6f

Nonce

510,450,597

Timestamp

11/8/2015, 11:15:26 AM

Confirmations

5,498,816

Mined by

⛏️ P2SHATbB9eAEiG96ghd3eAuPvBWz9LHUXZmx2m

Merkle Root

8268a96ca5ecde5a9da298ded61beedfaaf1fde996a25d90c3fd60e8503660ec
Transactions (2)
Coinbase1fcc2d8b362910…234e48d4e0c69e
1 in β†’ 1 out8.5300 XPM110 B
ATbB9eAE…HUXZmx2m
0a0fdf2cd39fd2…62152a6cd22158
29 in β†’ 2 out65.1212 XPM4.27 KB
AX7k7jMY…w8w84YaEAQHE5e6H…xDwU3vYU
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.049 Γ— 10⁹⁢(97-digit number)
20495832721564959936…46318932879870305281
Discovered Prime Numbers
p_k = 2^k Γ— 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
2.049 Γ— 10⁹⁢(97-digit number)
20495832721564959936…46318932879870305281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.099 Γ— 10⁹⁢(97-digit number)
40991665443129919873…92637865759740610561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.198 Γ— 10⁹⁢(97-digit number)
81983330886259839747…85275731519481221121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.639 Γ— 10⁹⁷(98-digit number)
16396666177251967949…70551463038962442241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.279 Γ— 10⁹⁷(98-digit number)
32793332354503935898…41102926077924884481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.558 Γ— 10⁹⁷(98-digit number)
65586664709007871797…82205852155849768961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.311 Γ— 10⁹⁸(99-digit number)
13117332941801574359…64411704311699537921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.623 Γ— 10⁹⁸(99-digit number)
26234665883603148719…28823408623399075841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.246 Γ— 10⁹⁸(99-digit number)
52469331767206297438…57646817246798151681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.049 Γ— 10⁹⁹(100-digit number)
10493866353441259487…15293634493596303361
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,781,507 XPMΒ·at block #6,817,183 Β· updates every 60s
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