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Block #1,042,710

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2015, 6:18:52 AM Β· Difficulty 10.7235 Β· 5,783,995 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ca1a10641107fee57a546b772ff6ba5949ce30d8080a44c8f48c9833fd0990ec
View on Chainz β†—

Height

#1,042,710

Difficulty

10.723472

Transactions

2

Size

399 B

Version

2

Bits

0ab93570

Nonce

667,342,056

Timestamp

5/3/2015, 6:18:52 AM

Confirmations

5,783,995

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

de50efb3bd88d512b13209bae6f9fc45567486dd8fd0059e661b10538f9b66fc
Transactions (2)
Coinbase5455082e01559e…4e0f89608f8ef2
1 in β†’ 1 out8.6900 XPM116 B
ANSXnLY2…Sd25TjkD
7518b8e95fb8fa…e6a5322d1c5f33
1 in β†’ 1 out99.9900 XPM192 B
AaNGD4rX…bpodGizP
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.

2.305 Γ— 10⁹⁢(97-digit number)
23054594800764257283…53179623629339473601
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
2.305 Γ— 10⁹⁢(97-digit number)
23054594800764257283…53179623629339473601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.610 Γ— 10⁹⁢(97-digit number)
46109189601528514567…06359247258678947201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.221 Γ— 10⁹⁢(97-digit number)
92218379203057029134…12718494517357894401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.844 Γ— 10⁹⁷(98-digit number)
18443675840611405826…25436989034715788801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.688 Γ— 10⁹⁷(98-digit number)
36887351681222811653…50873978069431577601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.377 Γ— 10⁹⁷(98-digit number)
73774703362445623307…01747956138863155201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.475 Γ— 10⁹⁸(99-digit number)
14754940672489124661…03495912277726310401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.950 Γ— 10⁹⁸(99-digit number)
29509881344978249323…06991824555452620801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.901 Γ— 10⁹⁸(99-digit number)
59019762689956498646…13983649110905241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.180 Γ— 10⁹⁹(100-digit number)
11803952537991299729…27967298221810483201
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:57,857,791 XPMΒ·at block #6,826,704 Β· updates every 60s
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