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Block #2,123,720

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2017, 11:06:24 AM Β· Difficulty 10.9171 Β· 4,684,200 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1b08d63fa124444d158febfc37189ef1842ede51ea42f363c75a752e661dc3d0
View on Chainz β†—

Height

#2,123,720

Difficulty

10.917074

Transactions

2

Size

1.39 KB

Version

2

Bits

0aeac55f

Nonce

166,578,205

Timestamp

5/19/2017, 11:06:24 AM

Confirmations

4,684,200

Mined by

⛏️ P2SHAWPqmgELKaa415ssGfW9sqE7tV4bmkk9fJ

Merkle Root

feb9b2a0d5d2e78e64b68edb2c8bec0462a194e126091c5d75f36a3a32250a2c
Transactions (2)
Coinbase730a1d467aa74e…e52a7fd4b9d862
1 in β†’ 1 out8.4000 XPM110 B
AWPqmgEL…4bmkk9fJ
5e94b852287566…9a9e6521897aeb
8 in β†’ 1 out797.9900 XPM1.20 KB
AcP3fxzU…CguEuPoM
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.

1.164 Γ— 10⁹⁡(96-digit number)
11646551450566728272…53206937691543213441
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
1.164 Γ— 10⁹⁡(96-digit number)
11646551450566728272…53206937691543213441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.329 Γ— 10⁹⁡(96-digit number)
23293102901133456544…06413875383086426881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.658 Γ— 10⁹⁡(96-digit number)
46586205802266913089…12827750766172853761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.317 Γ— 10⁹⁡(96-digit number)
93172411604533826179…25655501532345707521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.863 Γ— 10⁹⁢(97-digit number)
18634482320906765235…51311003064691415041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.726 Γ— 10⁹⁢(97-digit number)
37268964641813530471…02622006129382830081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.453 Γ— 10⁹⁢(97-digit number)
74537929283627060943…05244012258765660161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.490 Γ— 10⁹⁷(98-digit number)
14907585856725412188…10488024517531320321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.981 Γ— 10⁹⁷(98-digit number)
29815171713450824377…20976049035062640641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.963 Γ— 10⁹⁷(98-digit number)
59630343426901648755…41952098070125281281
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:57,707,395 XPMΒ·at block #6,807,919 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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