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Block #1,678,988

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2016, 9:00:02 PM Β· Difficulty 10.6971 Β· 5,154,107 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
458223fd7c07a605fe4713ef1a6a604f4f18fbe6bdb138016e48a1d411edbc05
View on Chainz β†—

Height

#1,678,988

Difficulty

10.697052

Transactions

2

Size

576 B

Version

2

Bits

0ab27207

Nonce

1,267,171,312

Timestamp

7/18/2016, 9:00:02 PM

Confirmations

5,154,107

Mined by

⛏️ P2SHAYwt58MmvikZkCdEV52x69dNvkv3EjmPEs

Merkle Root

44f1ed3a085a59dd1cb83b23a4e1e2e8cb55320ca9d6b82266c53c8864ab799c
Transactions (2)
Coinbasecd79b286e17b46…9995bed3a918be
1 in β†’ 1 out8.7400 XPM109 B
AYwt58Mm…v3EjmPEs
eb155575396ae5…146cb14dcf613a
2 in β†’ 2 out0.4986 XPM376 B
AGQoPA3Y…7Kz9WdrnAUFj5yWY…T6TWkAR1
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.

1.391 Γ— 10⁹⁢(97-digit number)
13919499786627643341…87201793276369203201
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
1.391 Γ— 10⁹⁢(97-digit number)
13919499786627643341…87201793276369203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.783 Γ— 10⁹⁢(97-digit number)
27838999573255286682…74403586552738406401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.567 Γ— 10⁹⁢(97-digit number)
55677999146510573365…48807173105476812801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.113 Γ— 10⁹⁷(98-digit number)
11135599829302114673…97614346210953625601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.227 Γ— 10⁹⁷(98-digit number)
22271199658604229346…95228692421907251201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.454 Γ— 10⁹⁷(98-digit number)
44542399317208458692…90457384843814502401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.908 Γ— 10⁹⁷(98-digit number)
89084798634416917384…80914769687629004801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.781 Γ— 10⁹⁸(99-digit number)
17816959726883383476…61829539375258009601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.563 Γ— 10⁹⁸(99-digit number)
35633919453766766953…23659078750516019201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.126 Γ— 10⁹⁸(99-digit number)
71267838907533533907…47318157501032038401
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:57,908,935 XPMΒ·at block #6,833,094 Β· updates every 60s
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