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Block #150,174

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/4/2013, 8:32:02 PM Β· Difficulty 9.8587 Β· 6,658,466 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e61235987d0b2f7183e144266e2f5dd4f7c6b7f3dda23f8669e18c62193a9f9
View on Chainz β†—

Height

#150,174

Difficulty

9.858725

Transactions

1

Size

198 B

Version

2

Bits

09dbd56f

Nonce

103,315

Timestamp

9/4/2013, 8:32:02 PM

Confirmations

6,658,466

Mined by

⛏️ P2SHAQDX4A7fYRFPkMLMMFvDCVebjcjoSW2gJw

Merkle Root

f359adb4fcacb7cc18b1b1d342bafb0ed34635f2c37dbbda48d22262e8edd7d3
Transactions (1)
Coinbasef359adb4fcacb7…d22262e8edd7d3
1 in β†’ 1 out10.2700 XPM109 B
AQDX4A7f…joSW2gJw
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.

4.044 Γ— 10⁹¹(92-digit number)
40440618499343249645…92530528355855241601
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
4.044 Γ— 10⁹¹(92-digit number)
40440618499343249645…92530528355855241601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.088 Γ— 10⁹¹(92-digit number)
80881236998686499291…85061056711710483201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.617 Γ— 10⁹²(93-digit number)
16176247399737299858…70122113423420966401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.235 Γ— 10⁹²(93-digit number)
32352494799474599716…40244226846841932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.470 Γ— 10⁹²(93-digit number)
64704989598949199433…80488453693683865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.294 Γ— 10⁹³(94-digit number)
12940997919789839886…60976907387367731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.588 Γ— 10⁹³(94-digit number)
25881995839579679773…21953814774735462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.176 Γ— 10⁹³(94-digit number)
51763991679159359546…43907629549470924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.035 Γ— 10⁹⁴(95-digit number)
10352798335831871909…87815259098941849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.070 Γ— 10⁹⁴(95-digit number)
20705596671663743818…75630518197883699201
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:57,713,171 XPMΒ·at block #6,808,639 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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