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Block #1,634,350

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/18/2016, 6:41:43 PM Β· Difficulty 10.6054 Β· 5,178,694 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
42c967437252ce4ed0055fc3a16612397cef3500a7adbd7d5d72ba7f691e6ab8
View on Chainz β†—

Height

#1,634,350

Difficulty

10.605425

Transactions

2

Size

12.09 KB

Version

2

Bits

0a9afd25

Nonce

129,471,750

Timestamp

6/18/2016, 6:41:43 PM

Confirmations

5,178,694

Mined by

⛏️ P2SHAT2D99A1nJyRKxBJCn5Krbo8a9XEJ2F4KF

Merkle Root

0fca5fae81b569fd7bd9ba7f44a740d974d9011f52a453e1233fdfa2c76a96a2
Transactions (2)
Coinbasebfee9329d194af…8b1ee6ceb31112
1 in β†’ 1 out9.3800 XPM109 B
AT2D99A1…XEJ2F4KF
8fc93c35bec23b…513736347205bc
82 in β†’ 1 out38.7880 XPM11.89 KB
AYpTr9AK…vVczSFU6
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.

1.555 Γ— 10⁹⁢(97-digit number)
15550498498744448333…68434140819488670721
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
1.555 Γ— 10⁹⁢(97-digit number)
15550498498744448333…68434140819488670721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.110 Γ— 10⁹⁢(97-digit number)
31100996997488896667…36868281638977341441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.220 Γ— 10⁹⁢(97-digit number)
62201993994977793335…73736563277954682881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.244 Γ— 10⁹⁷(98-digit number)
12440398798995558667…47473126555909365761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.488 Γ— 10⁹⁷(98-digit number)
24880797597991117334…94946253111818731521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.976 Γ— 10⁹⁷(98-digit number)
49761595195982234668…89892506223637463041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.952 Γ— 10⁹⁷(98-digit number)
99523190391964469336…79785012447274926081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.990 Γ— 10⁹⁸(99-digit number)
19904638078392893867…59570024894549852161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.980 Γ— 10⁹⁸(99-digit number)
39809276156785787734…19140049789099704321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.961 Γ— 10⁹⁸(99-digit number)
79618552313571575468…38280099578199408641
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:57,748,397 XPMΒ·at block #6,813,043 Β· updates every 60s
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