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Block #2,634,301

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 8:16:51 PM Β· Difficulty 11.2370 Β· 4,197,248 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2fa7953c5ccfc811045da6445d04700e1511afc79c04f3820b12cdcaa4f1d773
View on Chainz β†—

Height

#2,634,301

Difficulty

11.236994

Transactions

2

Size

576 B

Version

2

Bits

0b3caba7

Nonce

225,330,547

Timestamp

4/28/2018, 8:16:51 PM

Confirmations

4,197,248

Mined by

⛏️ P2SHAUiQa63xvzZ6zSDGVZ8RcCHLDpCoc85Za3

Merkle Root

fe7606804d41c81ed8bb4c48b19a671a6a8cf630b2b83ae81213d38ab163c090
Transactions (2)
Coinbase8a41c38c5a85f9…4fb9df667de0f6
1 in β†’ 1 out7.9200 XPM110 B
AUiQa63x…Coc85Za3
9beb750093426f…8ce091a476efde
2 in β†’ 2 out116.4725 XPM376 B
Ad3FmMmo…Qdw3toT4AR9ZmMv3…KoMtGjzo
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.

1.275 Γ— 10⁹⁡(96-digit number)
12759909604086446342…29161703859650072561
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
1.275 Γ— 10⁹⁡(96-digit number)
12759909604086446342…29161703859650072561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.551 Γ— 10⁹⁡(96-digit number)
25519819208172892684…58323407719300145121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.103 Γ— 10⁹⁡(96-digit number)
51039638416345785369…16646815438600290241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.020 Γ— 10⁹⁢(97-digit number)
10207927683269157073…33293630877200580481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.041 Γ— 10⁹⁢(97-digit number)
20415855366538314147…66587261754401160961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.083 Γ— 10⁹⁢(97-digit number)
40831710733076628295…33174523508802321921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.166 Γ— 10⁹⁢(97-digit number)
81663421466153256591…66349047017604643841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.633 Γ— 10⁹⁷(98-digit number)
16332684293230651318…32698094035209287681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.266 Γ— 10⁹⁷(98-digit number)
32665368586461302636…65396188070418575361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.533 Γ— 10⁹⁷(98-digit number)
65330737172922605273…30792376140837150721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.306 Γ— 10⁹⁸(99-digit number)
13066147434584521054…61584752281674301441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,896,483 XPMΒ·at block #6,831,548 Β· updates every 60s
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