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Block #2,272,062

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/28/2017, 4:01:45 PM Β· Difficulty 10.9540 Β· 4,570,665 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cf85467bbf5db0df108f1e1096651da028e8e2880b276a36901e4fd87feb7a3e
View on Chainz β†—

Height

#2,272,062

Difficulty

10.953989

Transactions

1

Size

198 B

Version

2

Bits

0af4389f

Nonce

52,955,021

Timestamp

8/28/2017, 4:01:45 PM

Confirmations

4,570,665

Mined by

⛏️ P2SHANVQknnPd1Za8tiff4onCp4pxCqWZtaKdy

Merkle Root

608fcd6b6cc8e0d094d4554cefc29404dce6799a19d79b5a9bbc3e18ee2233ce
Transactions (1)
Coinbase608fcd6b6cc8e0…bc3e18ee2233ce
1 in β†’ 1 out8.3200 XPM109 B
ANVQknnP…qWZtaKdy
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.

1.705 Γ— 10⁹²(93-digit number)
17058428752280629887…94402965777064553441
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
1.705 Γ— 10⁹²(93-digit number)
17058428752280629887…94402965777064553441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.411 Γ— 10⁹²(93-digit number)
34116857504561259774…88805931554129106881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.823 Γ— 10⁹²(93-digit number)
68233715009122519548…77611863108258213761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.364 Γ— 10⁹³(94-digit number)
13646743001824503909…55223726216516427521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.729 Γ— 10⁹³(94-digit number)
27293486003649007819…10447452433032855041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.458 Γ— 10⁹³(94-digit number)
54586972007298015638…20894904866065710081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.091 Γ— 10⁹⁴(95-digit number)
10917394401459603127…41789809732131420161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.183 Γ— 10⁹⁴(95-digit number)
21834788802919206255…83579619464262840321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.366 Γ— 10⁹⁴(95-digit number)
43669577605838412510…67159238928525680641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.733 Γ— 10⁹⁴(95-digit number)
87339155211676825021…34318477857051361281
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:57,986,155 XPMΒ·at block #6,842,726 Β· updates every 60s
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