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Block #184,991

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2013, 12:04:11 AM Β· Difficulty 9.8621 Β· 6,622,597 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
06ae38b47aae2d6d8f7e7eb94ebbe7463fef8d51ebe9b8a2f21b05f254e58f9f
View on Chainz β†—

Height

#184,991

Difficulty

9.862056

Transactions

1

Size

196 B

Version

2

Bits

09dcafb7

Nonce

120,592

Timestamp

9/29/2013, 12:04:11 AM

Confirmations

6,622,597

Mined by

⛏️ P2SHAah59eDE19nFdT81huVknfjPafNny9AgXr

Merkle Root

cedb1a0b424bba94d3a33dd47de0ca36c43712910fb08bbf246b25d11c8de1b1
Transactions (1)
Coinbasecedb1a0b424bba…6b25d11c8de1b1
1 in β†’ 1 out10.2700 XPM109 B
Aah59eDE…Nny9AgXr
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.

6.173 Γ— 10⁸⁷(88-digit number)
61737601215294883608…04626406828847109041
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
6.173 Γ— 10⁸⁷(88-digit number)
61737601215294883608…04626406828847109041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.234 Γ— 10⁸⁸(89-digit number)
12347520243058976721…09252813657694218081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.469 Γ— 10⁸⁸(89-digit number)
24695040486117953443…18505627315388436161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.939 Γ— 10⁸⁸(89-digit number)
49390080972235906886…37011254630776872321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.878 Γ— 10⁸⁸(89-digit number)
98780161944471813773…74022509261553744641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.975 Γ— 10⁸⁹(90-digit number)
19756032388894362754…48045018523107489281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.951 Γ— 10⁸⁹(90-digit number)
39512064777788725509…96090037046214978561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.902 Γ— 10⁸⁹(90-digit number)
79024129555577451018…92180074092429957121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.580 Γ— 10⁹⁰(91-digit number)
15804825911115490203…84360148184859914241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.160 Γ— 10⁹⁰(91-digit number)
31609651822230980407…68720296369719828481
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:57,704,731 XPMΒ·at block #6,807,587 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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