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Block #1,313,528

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/5/2015, 7:08:21 AM Β· Difficulty 10.8555 Β· 5,494,684 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dc625d6d7a6b85e45a1d0e747e86a89a61d4713fe51c1eb2ac44ae525e24aed0
View on Chainz β†—

Height

#1,313,528

Difficulty

10.855453

Transactions

2

Size

12.23 KB

Version

2

Bits

0adafef3

Nonce

1,403,791,162

Timestamp

11/5/2015, 7:08:21 AM

Confirmations

5,494,684

Mined by

⛏️ P2SHAakrt8Yajra9iXkuWGvjeQXGNKKNGe7CAB

Merkle Root

c99b8d457366b7248ed9f1c2711412faf49694df436b1ce906f33acb424803a7
Transactions (2)
Coinbase1022b1c21a9842…998ed0570ffba3
1 in β†’ 1 out8.7400 XPM110 B
Aakrt8Ya…KNGe7CAB
9bad397b5da057…8fe12cad9cdbd7
83 in β†’ 1 out1753.3401 XPM12.03 KB
AQHE5e6H…xDwU3vYU
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.

3.856 Γ— 10⁹⁢(97-digit number)
38568692391707481655…39953565170770955521
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
3.856 Γ— 10⁹⁢(97-digit number)
38568692391707481655…39953565170770955521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.713 Γ— 10⁹⁢(97-digit number)
77137384783414963311…79907130341541911041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.542 Γ— 10⁹⁷(98-digit number)
15427476956682992662…59814260683083822081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.085 Γ— 10⁹⁷(98-digit number)
30854953913365985324…19628521366167644161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.170 Γ— 10⁹⁷(98-digit number)
61709907826731970649…39257042732335288321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.234 Γ— 10⁹⁸(99-digit number)
12341981565346394129…78514085464670576641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.468 Γ— 10⁹⁸(99-digit number)
24683963130692788259…57028170929341153281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.936 Γ— 10⁹⁸(99-digit number)
49367926261385576519…14056341858682306561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.873 Γ— 10⁹⁸(99-digit number)
98735852522771153038…28112683717364613121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.974 Γ— 10⁹⁹(100-digit number)
19747170504554230607…56225367434729226241
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:57,709,747 XPMΒ·at block #6,808,211 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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