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Block #2,008,090

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/4/2017, 1:08:45 PM Β· Difficulty 10.7010 Β· 4,834,699 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f32e80d309ee104218d26558b698e20c9cf8008412b9ab773f34f96dbab0e5de
View on Chainz β†—

Height

#2,008,090

Difficulty

10.701006

Transactions

1

Size

201 B

Version

2

Bits

0ab37527

Nonce

201,986,682

Timestamp

3/4/2017, 1:08:45 PM

Confirmations

4,834,699

Mined by

⛏️ P2SHARr9ZjWbV6z9pRX1hPNMNsrYrDhujnkDMy

Merkle Root

b6f11f139f44950f1b6f5b8548ca2c7d7e920463a212dc47f27547ae614fea5c
Transactions (1)
Coinbaseb6f11f139f4495…7547ae614fea5c
1 in β†’ 1 out8.7200 XPM110 B
ARr9ZjWb…hujnkDMy
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.

2.921 Γ— 10⁹⁢(97-digit number)
29212877669208048239…48345420391704350719
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
2.921 Γ— 10⁹⁢(97-digit number)
29212877669208048239…48345420391704350719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.842 Γ— 10⁹⁢(97-digit number)
58425755338416096479…96690840783408701439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁷(98-digit number)
11685151067683219295…93381681566817402879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.337 Γ— 10⁹⁷(98-digit number)
23370302135366438591…86763363133634805759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.674 Γ— 10⁹⁷(98-digit number)
46740604270732877183…73526726267269611519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.348 Γ— 10⁹⁷(98-digit number)
93481208541465754366…47053452534539223039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁸(99-digit number)
18696241708293150873…94106905069078446079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.739 Γ— 10⁹⁸(99-digit number)
37392483416586301746…88213810138156892159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.478 Γ— 10⁹⁸(99-digit number)
74784966833172603493…76427620276313784319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.495 Γ— 10⁹⁹(100-digit number)
14956993366634520698…52855240552627568639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.991 Γ— 10⁹⁹(100-digit number)
29913986733269041397…05710481105255137279
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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