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Block #1,611,257

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2016, 5:24:40 PM Β· Difficulty 10.6063 Β· 5,232,838 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
419c4f4d584f783fa6edce7cb8bdf3d8ba865a1f5863b33fdba0d34148ff86ca
View on Chainz β†—

Height

#1,611,257

Difficulty

10.606303

Transactions

1

Size

200 B

Version

2

Bits

0a9b36a6

Nonce

168,242,897

Timestamp

6/2/2016, 5:24:40 PM

Confirmations

5,232,838

Mined by

⛏️ P2SHAdNnRMX2hwDMr7dkSC9dnE6EMsUxpqKS86

Merkle Root

75f45f3231395cbd441a8d230bae3c0ebae38c19e26225fb4c57a9c85457e0bf
Transactions (1)
Coinbase75f45f3231395c…57a9c85457e0bf
1 in β†’ 1 out8.8800 XPM109 B
AdNnRMX2…UxpqKS86
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.

2.098 Γ— 10⁹⁢(97-digit number)
20987550777048524374…82834798363134686721
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
2.098 Γ— 10⁹⁢(97-digit number)
20987550777048524374…82834798363134686721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.197 Γ— 10⁹⁢(97-digit number)
41975101554097048748…65669596726269373441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.395 Γ— 10⁹⁢(97-digit number)
83950203108194097497…31339193452538746881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.679 Γ— 10⁹⁷(98-digit number)
16790040621638819499…62678386905077493761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.358 Γ— 10⁹⁷(98-digit number)
33580081243277638998…25356773810154987521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.716 Γ— 10⁹⁷(98-digit number)
67160162486555277997…50713547620309975041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.343 Γ— 10⁹⁸(99-digit number)
13432032497311055599…01427095240619950081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.686 Γ— 10⁹⁸(99-digit number)
26864064994622111199…02854190481239900161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.372 Γ— 10⁹⁸(99-digit number)
53728129989244222398…05708380962479800321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.074 Γ— 10⁹⁹(100-digit number)
10745625997848844479…11416761924959600641
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:57,997,134 XPMΒ·at block #6,844,094 Β· updates every 60s
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