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Block #1,534,532

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2016, 7:37:06 AM Β· Difficulty 10.6169 Β· 5,282,241 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
efa4d75798174331ed029e36db4cc038881196da9805076565e16944f5502038
View on Chainz β†—

Height

#1,534,532

Difficulty

10.616889

Transactions

2

Size

7.60 KB

Version

2

Bits

0a9dec71

Nonce

790,703,730

Timestamp

4/10/2016, 7:37:06 AM

Confirmations

5,282,241

Mined by

⛏️ P2SHAS6AxeZ9vq1eYtdmbKsh5B7iv7J142GiKZ

Merkle Root

5edaf7fd47437c1fbfb63384e4852ab4f8db080cc6d1238c1d08f0fe40be46da
Transactions (2)
Coinbase58848191a87c0e…e3e1be458890cc
1 in β†’ 1 out8.9400 XPM109 B
AS6AxeZ9…J142GiKZ
7cbad614ed4e46…43570aa4ad5bce
51 in β†’ 1 out1161.3032 XPM7.41 KB
ALnxkxL8…mCnaGgJt
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.

1.209 Γ— 10⁹⁢(97-digit number)
12094197420243193874…30169551281887641601
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
1.209 Γ— 10⁹⁢(97-digit number)
12094197420243193874…30169551281887641601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.418 Γ— 10⁹⁢(97-digit number)
24188394840486387748…60339102563775283201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.837 Γ— 10⁹⁢(97-digit number)
48376789680972775496…20678205127550566401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.675 Γ— 10⁹⁢(97-digit number)
96753579361945550993…41356410255101132801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.935 Γ— 10⁹⁷(98-digit number)
19350715872389110198…82712820510202265601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.870 Γ— 10⁹⁷(98-digit number)
38701431744778220397…65425641020404531201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.740 Γ— 10⁹⁷(98-digit number)
77402863489556440794…30851282040809062401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.548 Γ— 10⁹⁸(99-digit number)
15480572697911288158…61702564081618124801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.096 Γ— 10⁹⁸(99-digit number)
30961145395822576317…23405128163236249601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.192 Γ— 10⁹⁸(99-digit number)
61922290791645152635…46810256326472499201
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:57,778,218 XPMΒ·at block #6,816,772 Β· updates every 60s
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