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Block #636,143

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/16/2014, 5:15:44 PM Β· Difficulty 10.9639 Β· 6,195,581 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cd61fbaa72f990ea5c73c199b8487762c2ebe30d86123b8f1b53cee94b3c119c
View on Chainz β†—

Height

#636,143

Difficulty

10.963868

Transactions

1

Size

207 B

Version

2

Bits

0af6c00a

Nonce

1,695,987,240

Timestamp

7/16/2014, 5:15:44 PM

Confirmations

6,195,581

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5233d77b0e8544c9eb6e64631d6e71c6aaa257db6b4ed2669edfd6c4e1bce9d5
Transactions (1)
Coinbase5233d77b0e8544…dfd6c4e1bce9d5
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.000 Γ— 10⁹⁷(98-digit number)
10006172719106575996…77005029595127101441
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
1.000 Γ— 10⁹⁷(98-digit number)
10006172719106575996…77005029595127101441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.001 Γ— 10⁹⁷(98-digit number)
20012345438213151993…54010059190254202881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.002 Γ— 10⁹⁷(98-digit number)
40024690876426303986…08020118380508405761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.004 Γ— 10⁹⁷(98-digit number)
80049381752852607972…16040236761016811521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.600 Γ— 10⁹⁸(99-digit number)
16009876350570521594…32080473522033623041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.201 Γ— 10⁹⁸(99-digit number)
32019752701141043188…64160947044067246081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.403 Γ— 10⁹⁸(99-digit number)
64039505402282086377…28321894088134492161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.280 Γ— 10⁹⁹(100-digit number)
12807901080456417275…56643788176268984321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.561 Γ— 10⁹⁹(100-digit number)
25615802160912834551…13287576352537968641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.123 Γ— 10⁹⁹(100-digit number)
51231604321825669102…26575152705075937281
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:57,897,897 XPMΒ·at block #6,831,723 Β· updates every 60s
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