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Block #1,368,444

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2015, 10:52:01 PM Β· Difficulty 10.8344 Β· 5,474,167 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f99d3330320f3fdc2fbe485bff5eae8444b0d7dbebc31a83db5fbfc47d54171c
View on Chainz β†—

Height

#1,368,444

Difficulty

10.834431

Transactions

1

Size

199 B

Version

2

Bits

0ad59d4d

Nonce

1,356,313,147

Timestamp

12/13/2015, 10:52:01 PM

Confirmations

5,474,167

Mined by

⛏️ P2SHANgr5KiP3uh1oZoy3Wuv7nA1EcZpi8e91S

Merkle Root

0daec9372a79b76c769f6639e410e5e13fe271eb4274d4526aa5604eb0c84d04
Transactions (1)
Coinbase0daec9372a79b7…a5604eb0c84d04
1 in β†’ 1 out8.5100 XPM109 B
ANgr5KiP…Zpi8e91S
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.

2.737 Γ— 10⁹⁡(96-digit number)
27378841236519739564…07491065587121539201
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
2.737 Γ— 10⁹⁡(96-digit number)
27378841236519739564…07491065587121539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.475 Γ— 10⁹⁡(96-digit number)
54757682473039479129…14982131174243078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.095 Γ— 10⁹⁢(97-digit number)
10951536494607895825…29964262348486156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.190 Γ— 10⁹⁢(97-digit number)
21903072989215791651…59928524696972313601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.380 Γ— 10⁹⁢(97-digit number)
43806145978431583303…19857049393944627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.761 Γ— 10⁹⁢(97-digit number)
87612291956863166606…39714098787889254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.752 Γ— 10⁹⁷(98-digit number)
17522458391372633321…79428197575778508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.504 Γ— 10⁹⁷(98-digit number)
35044916782745266642…58856395151557017601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.008 Γ— 10⁹⁷(98-digit number)
70089833565490533285…17712790303114035201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.401 Γ— 10⁹⁸(99-digit number)
14017966713098106657…35425580606228070401
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:57,985,318 XPMΒ·at block #6,842,610 Β· updates every 60s
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