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Block #161,946

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2013, 11:54:30 PM Β· Difficulty 9.8606 Β· 6,646,361 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4d7b62b0a601409452cfe0b139b1e4f3dc020f3680db7c45295d2f02e2d4a941
View on Chainz β†—

Height

#161,946

Difficulty

9.860648

Transactions

1

Size

198 B

Version

2

Bits

09dc5373

Nonce

622,639

Timestamp

9/12/2013, 11:54:30 PM

Confirmations

6,646,361

Mined by

⛏️ P2SHAdDUNTYmz3S4v6JdhjgL2fyWhUv4Zjqa77

Merkle Root

300ffe998e53bf203f95bd6484dab50a7f29e68215da3e6d45724c50fec7ebf0
Transactions (1)
Coinbase300ffe998e53bf…724c50fec7ebf0
1 in β†’ 1 out10.2700 XPM109 B
AdDUNTYm…v4Zjqa77
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.

5.771 Γ— 10⁹¹(92-digit number)
57718608789609786986…36647552232608878881
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
5.771 Γ— 10⁹¹(92-digit number)
57718608789609786986…36647552232608878881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.154 Γ— 10⁹²(93-digit number)
11543721757921957397…73295104465217757761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.308 Γ— 10⁹²(93-digit number)
23087443515843914794…46590208930435515521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.617 Γ— 10⁹²(93-digit number)
46174887031687829589…93180417860871031041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.234 Γ— 10⁹²(93-digit number)
92349774063375659178…86360835721742062081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.846 Γ— 10⁹³(94-digit number)
18469954812675131835…72721671443484124161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.693 Γ— 10⁹³(94-digit number)
36939909625350263671…45443342886968248321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.387 Γ— 10⁹³(94-digit number)
73879819250700527342…90886685773936496641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.477 Γ— 10⁹⁴(95-digit number)
14775963850140105468…81773371547872993281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.955 Γ— 10⁹⁴(95-digit number)
29551927700280210937…63546743095745986561
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:57,710,511 XPMΒ·at block #6,808,306 Β· updates every 60s
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