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Block #1,368,447

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2015, 10:57:53 PM Β· Difficulty 10.8344 Β· 5,471,763 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0b9d36bff32ba6a7ea715bee74d5e8cc402962c8ceab5736a7ab8a9b5fadf331
View on Chainz β†—

Height

#1,368,447

Difficulty

10.834385

Transactions

1

Size

200 B

Version

2

Bits

0ad59a42

Nonce

70,865,777

Timestamp

12/13/2015, 10:57:53 PM

Confirmations

5,471,763

Mined by

⛏️ P2SHANgaE9UGfG65CiXEYqeWZ1pHfkAB8yifxK

Merkle Root

51ff99cb97f57f85e49c00a695771bcb18ea11382104adbb19db0688b397d27c
Transactions (1)
Coinbase51ff99cb97f57f…db0688b397d27c
1 in β†’ 1 out8.5100 XPM110 B
ANgaE9UG…AB8yifxK
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.

7.028 Γ— 10⁹⁴(95-digit number)
70282461729653353085…09907222742133912001
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
7.028 Γ— 10⁹⁴(95-digit number)
70282461729653353085…09907222742133912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.405 Γ— 10⁹⁡(96-digit number)
14056492345930670617…19814445484267824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.811 Γ— 10⁹⁡(96-digit number)
28112984691861341234…39628890968535648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.622 Γ— 10⁹⁡(96-digit number)
56225969383722682468…79257781937071296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.124 Γ— 10⁹⁢(97-digit number)
11245193876744536493…58515563874142592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.249 Γ— 10⁹⁢(97-digit number)
22490387753489072987…17031127748285184001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.498 Γ— 10⁹⁢(97-digit number)
44980775506978145974…34062255496570368001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.996 Γ— 10⁹⁢(97-digit number)
89961551013956291949…68124510993140736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.799 Γ— 10⁹⁷(98-digit number)
17992310202791258389…36249021986281472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.598 Γ— 10⁹⁷(98-digit number)
35984620405582516779…72498043972562944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.196 Γ— 10⁹⁷(98-digit number)
71969240811165033559…44996087945125888001
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,965,998 XPMΒ·at block #6,840,209 Β· updates every 60s
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