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Block #1,717,607

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/15/2016, 1:39:25 AM Β· Difficulty 10.6643 Β· 5,079,260 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
16d0a3f048a469a6c9b2271a795b3d1c9982263a4e4280f2397c7380533b4715
View on Chainz β†—

Height

#1,717,607

Difficulty

10.664334

Transactions

1

Size

243 B

Version

2

Bits

0aaa11cc

Nonce

806,185,926

Timestamp

8/15/2016, 1:39:25 AM

Confirmations

5,079,260

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

7b3d2a18c64d08721a974ba9418cd63246789fbde7c088d5e96fe4cfbbcb3413
Transactions (1)
Coinbase7b3d2a18c64d08…6fe4cfbbcb3413
1 in β†’ 2 out8.7800 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

8.704 Γ— 10⁹⁢(97-digit number)
87046004341047602181…45025866250912430081
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
8.704 Γ— 10⁹⁢(97-digit number)
87046004341047602181…45025866250912430081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.740 Γ— 10⁹⁷(98-digit number)
17409200868209520436…90051732501824860161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.481 Γ— 10⁹⁷(98-digit number)
34818401736419040872…80103465003649720321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.963 Γ— 10⁹⁷(98-digit number)
69636803472838081745…60206930007299440641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.392 Γ— 10⁹⁸(99-digit number)
13927360694567616349…20413860014598881281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.785 Γ— 10⁹⁸(99-digit number)
27854721389135232698…40827720029197762561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.570 Γ— 10⁹⁸(99-digit number)
55709442778270465396…81655440058395525121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.114 Γ— 10⁹⁹(100-digit number)
11141888555654093079…63310880116791050241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.228 Γ— 10⁹⁹(100-digit number)
22283777111308186158…26621760233582100481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.456 Γ— 10⁹⁹(100-digit number)
44567554222616372316…53243520467164200961
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:57,618,951 XPMΒ·at block #6,796,866 Β· updates every 60s
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