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Block #2,009,610

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/5/2017, 2:50:27 PM Β· Difficulty 10.6995 Β· 4,817,294 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b06424121e1de11f997082ff4ad2e3ab2030651ac0ef4d0aec5ad9e911d7697
View on Chainz β†—

Height

#2,009,610

Difficulty

10.699537

Transactions

1

Size

200 B

Version

2

Bits

0ab314db

Nonce

174,545

Timestamp

3/5/2017, 2:50:27 PM

Confirmations

4,817,294

Mined by

⛏️ P2SHARaPyHgjo2zpePAfC2xk8aeQGMnA9veLYH

Merkle Root

96236e8e14de11493c2d29762d196841a6a212ee30a4b0a712efd80dd773e576
Transactions (1)
Coinbase96236e8e14de11…efd80dd773e576
1 in β†’ 1 out8.7200 XPM109 B
ARaPyHgj…nA9veLYH
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.

1.347 Γ— 10⁹⁸(99-digit number)
13474069797345784553…25680652806571683161
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
1.347 Γ— 10⁹⁸(99-digit number)
13474069797345784553…25680652806571683161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.694 Γ— 10⁹⁸(99-digit number)
26948139594691569106…51361305613143366321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.389 Γ— 10⁹⁸(99-digit number)
53896279189383138213…02722611226286732641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.077 Γ— 10⁹⁹(100-digit number)
10779255837876627642…05445222452573465281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.155 Γ— 10⁹⁹(100-digit number)
21558511675753255285…10890444905146930561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.311 Γ— 10⁹⁹(100-digit number)
43117023351506510570…21780889810293861121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.623 Γ— 10⁹⁹(100-digit number)
86234046703013021141…43561779620587722241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.724 Γ— 10¹⁰⁰(101-digit number)
17246809340602604228…87123559241175444481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.449 Γ— 10¹⁰⁰(101-digit number)
34493618681205208456…74247118482350888961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.898 Γ— 10¹⁰⁰(101-digit number)
68987237362410416913…48494236964701777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.379 Γ— 10¹⁰¹(102-digit number)
13797447472482083382…96988473929403555841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,859,399 XPMΒ·at block #6,826,903 Β· updates every 60s
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