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Block #1,471,106

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/25/2016, 5:03:02 AM Β· Difficulty 10.7148 Β· 5,373,294 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
60688bd45efa4ea0826032e491ca15dbb8a40a2972515889daa3511a4091b285
View on Chainz β†—

Height

#1,471,106

Difficulty

10.714783

Transactions

1

Size

198 B

Version

2

Bits

0ab6fc0c

Nonce

435,594,654

Timestamp

2/25/2016, 5:03:02 AM

Confirmations

5,373,294

Mined by

⛏️ P2SHAdTCbSwENjefEqxwDKKfh7hzPBQ7moJK4W

Merkle Root

e38762b453363cba25880d34958b0ac7cb2d526415ef4f1f198f38b8884c2533
Transactions (1)
Coinbasee38762b453363c…8f38b8884c2533
1 in β†’ 1 out8.7000 XPM109 B
AdTCbSwE…Q7moJK4W
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.

1.014 Γ— 10⁹³(94-digit number)
10148562485454054262…52032203850613775681
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
1.014 Γ— 10⁹³(94-digit number)
10148562485454054262…52032203850613775681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.029 Γ— 10⁹³(94-digit number)
20297124970908108524…04064407701227551361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.059 Γ— 10⁹³(94-digit number)
40594249941816217048…08128815402455102721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.118 Γ— 10⁹³(94-digit number)
81188499883632434096…16257630804910205441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.623 Γ— 10⁹⁴(95-digit number)
16237699976726486819…32515261609820410881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.247 Γ— 10⁹⁴(95-digit number)
32475399953452973638…65030523219640821761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.495 Γ— 10⁹⁴(95-digit number)
64950799906905947277…30061046439281643521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.299 Γ— 10⁹⁡(96-digit number)
12990159981381189455…60122092878563287041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.598 Γ— 10⁹⁡(96-digit number)
25980319962762378910…20244185757126574081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.196 Γ— 10⁹⁡(96-digit number)
51960639925524757821…40488371514253148161
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:57,999,592 XPMΒ·at block #6,844,399 Β· updates every 60s
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