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Block #1,102,617

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/13/2015, 10:46:52 AM Β· Difficulty 10.7564 Β· 5,691,902 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7dc304c6f6af3eb870990aa647d9020e4d456301360e969cab0b58d3511e6e2b
View on Chainz β†—

Height

#1,102,617

Difficulty

10.756444

Transactions

2

Size

84.06 KB

Version

2

Bits

0ac1a648

Nonce

223,686,346

Timestamp

6/13/2015, 10:46:52 AM

Confirmations

5,691,902

Mined by

⛏️ P2SHAbauTfUqGLBZcsg5PZJYsXn9u2H6kk9rCp

Merkle Root

5eee8160da6bf84d716c43bb4e855897b79126ae171c13944fb8bef04bd05157
Transactions (2)
Coinbase83fc0dfdbcce02…eb580c1eb10dc7
1 in β†’ 1 out9.4900 XPM109 B
AbauTfUq…H6kk9rCp
2586526af0dbcc…0544bb51311ec5
580 in β†’ 2 out3000.0100 XPM83.87 KB
AegqTC97…VEiZooN2AQBsf9af…By2wPxE3
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.

2.209 Γ— 10⁹⁴(95-digit number)
22096572358587388085…18752053293110085601
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
2.209 Γ— 10⁹⁴(95-digit number)
22096572358587388085…18752053293110085601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.419 Γ— 10⁹⁴(95-digit number)
44193144717174776171…37504106586220171201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.838 Γ— 10⁹⁴(95-digit number)
88386289434349552343…75008213172440342401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.767 Γ— 10⁹⁡(96-digit number)
17677257886869910468…50016426344880684801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.535 Γ— 10⁹⁡(96-digit number)
35354515773739820937…00032852689761369601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.070 Γ— 10⁹⁡(96-digit number)
70709031547479641874…00065705379522739201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.414 Γ— 10⁹⁢(97-digit number)
14141806309495928374…00131410759045478401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.828 Γ— 10⁹⁢(97-digit number)
28283612618991856749…00262821518090956801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.656 Γ— 10⁹⁢(97-digit number)
56567225237983713499…00525643036181913601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.131 Γ— 10⁹⁷(98-digit number)
11313445047596742699…01051286072363827201
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:57,600,190 XPMΒ·at block #6,794,518 Β· updates every 60s
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