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Block #2,038,868

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/26/2017, 3:59:43 AM Β· Difficulty 10.6807 Β· 4,803,035 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5dd236706e4cf3d50dc6d2b0a616a33eb72e0552d47d8f2c1926e6dfce233b21
View on Chainz β†—

Height

#2,038,868

Difficulty

10.680724

Transactions

2

Size

5.74 KB

Version

2

Bits

0aae43ee

Nonce

278,849,941

Timestamp

3/26/2017, 3:59:43 AM

Confirmations

4,803,035

Mined by

⛏️ P2SHAWWm12RhCbN93F5kZwjVqcYYoJVDrjbHwU

Merkle Root

71e350521d4aedd9207520c4c7e8f35cafb2f40fb9922944311671de182cc8bf
Transactions (2)
Coinbasee592702b612280…c111f35b7b2460
1 in β†’ 1 out8.8100 XPM109 B
AWWm12Rh…VDrjbHwU
7f89e58602f4d2…fd3db10e5fe819
38 in β†’ 1 out1.6836 XPM5.54 KB
AWKCXX8y…hkvG73UE
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.

1.231 Γ— 10⁹⁡(96-digit number)
12314991400530604138…54370294579545265121
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
1.231 Γ— 10⁹⁡(96-digit number)
12314991400530604138…54370294579545265121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.462 Γ— 10⁹⁡(96-digit number)
24629982801061208277…08740589159090530241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.925 Γ— 10⁹⁡(96-digit number)
49259965602122416554…17481178318181060481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.851 Γ— 10⁹⁡(96-digit number)
98519931204244833109…34962356636362120961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.970 Γ— 10⁹⁢(97-digit number)
19703986240848966621…69924713272724241921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.940 Γ— 10⁹⁢(97-digit number)
39407972481697933243…39849426545448483841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.881 Γ— 10⁹⁢(97-digit number)
78815944963395866487…79698853090896967681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.576 Γ— 10⁹⁷(98-digit number)
15763188992679173297…59397706181793935361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.152 Γ— 10⁹⁷(98-digit number)
31526377985358346594…18795412363587870721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.305 Γ— 10⁹⁷(98-digit number)
63052755970716693189…37590824727175741441
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:57,979,598 XPMΒ·at block #6,841,902 Β· updates every 60s
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