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Block #3,503,921

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/7/2020, 1:23:33 PM Β· Difficulty 10.9309 Β· 3,336,218 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76d050d5321cd39fb4b9be1a5402f32a9ce0879ad534433b38a149cc8ac21248
View on Chainz β†—

Height

#3,503,921

Difficulty

10.930885

Transactions

2

Size

7.46 KB

Version

2

Bits

0aee4e78

Nonce

9,527,901

Timestamp

1/7/2020, 1:23:33 PM

Confirmations

3,336,218

Mined by

⛏️ P2SHAa32y8PQmrraS9AMzCsmSNxawTe3Enbehj

Merkle Root

f786c61590d17bf79b613238c73d135716e392229ec1bfe46f81018bc7bf44c0
Transactions (2)
Coinbase78bb6bc92fbc01…bb3f39c8c23352
1 in β†’ 1 out8.4400 XPM109 B
Aa32y8PQ…e3Enbehj
2e50d3ba1df875…76941294cd0adb
50 in β†’ 1 out249.9200 XPM7.26 KB
ALcTQaSP…1C5Yf2Zi
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.

1.143 Γ— 10⁹⁷(98-digit number)
11432306622348084386…42995230791809670401
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
1.143 Γ— 10⁹⁷(98-digit number)
11432306622348084386…42995230791809670401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.286 Γ— 10⁹⁷(98-digit number)
22864613244696168773…85990461583619340801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.572 Γ— 10⁹⁷(98-digit number)
45729226489392337547…71980923167238681601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.145 Γ— 10⁹⁷(98-digit number)
91458452978784675094…43961846334477363201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.829 Γ— 10⁹⁸(99-digit number)
18291690595756935018…87923692668954726401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.658 Γ— 10⁹⁸(99-digit number)
36583381191513870037…75847385337909452801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.316 Γ— 10⁹⁸(99-digit number)
73166762383027740075…51694770675818905601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.463 Γ— 10⁹⁹(100-digit number)
14633352476605548015…03389541351637811201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.926 Γ— 10⁹⁹(100-digit number)
29266704953211096030…06779082703275622401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.853 Γ— 10⁹⁹(100-digit number)
58533409906422192060…13558165406551244801
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:57,965,428 XPMΒ·at block #6,840,138 Β· updates every 60s
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