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Block #2,476,320

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/16/2018, 10:08:14 PM Β· Difficulty 10.9644 Β· 4,368,978 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7eec879a172e97f1d0057a76949ae8702927666bf4d29cd8b4e739880ac7d0cf
View on Chainz β†—

Height

#2,476,320

Difficulty

10.964417

Transactions

1

Size

201 B

Version

2

Bits

0af6e401

Nonce

1,312,800,782

Timestamp

1/16/2018, 10:08:14 PM

Confirmations

4,368,978

Mined by

⛏️ P2SHAe4bHWrTVc9Bf6sVopawca19vKRo6amJz1

Merkle Root

24a8c313b965107f77f17b8570e1e59608a7999ff39be58c53f39e1383db25aa
Transactions (1)
Coinbase24a8c313b96510…f39e1383db25aa
1 in β†’ 1 out8.3000 XPM110 B
Ae4bHWrT…Ro6amJz1
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.

9.663 Γ— 10⁹⁡(96-digit number)
96632360323206427809…59440835786016189441
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
9.663 Γ— 10⁹⁡(96-digit number)
96632360323206427809…59440835786016189441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.932 Γ— 10⁹⁢(97-digit number)
19326472064641285561…18881671572032378881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.865 Γ— 10⁹⁢(97-digit number)
38652944129282571123…37763343144064757761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.730 Γ— 10⁹⁢(97-digit number)
77305888258565142247…75526686288129515521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.546 Γ— 10⁹⁷(98-digit number)
15461177651713028449…51053372576259031041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.092 Γ— 10⁹⁷(98-digit number)
30922355303426056899…02106745152518062081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.184 Γ— 10⁹⁷(98-digit number)
61844710606852113798…04213490305036124161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.236 Γ— 10⁹⁸(99-digit number)
12368942121370422759…08426980610072248321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.473 Γ— 10⁹⁸(99-digit number)
24737884242740845519…16853961220144496641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.947 Γ— 10⁹⁸(99-digit number)
49475768485481691038…33707922440288993281
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:58,006,823 XPMΒ·at block #6,845,297 Β· updates every 60s
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