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Block #2,050,724

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/3/2017, 5:46:06 AM Β· Difficulty 10.6967 Β· 4,789,923 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2b3aee682001afee74d8bc3a6492271a4cec32372925eebdea534c0d40e64dd5
View on Chainz β†—

Height

#2,050,724

Difficulty

10.696715

Transactions

2

Size

7.93 KB

Version

2

Bits

0ab25bee

Nonce

293,132,938

Timestamp

4/3/2017, 5:46:06 AM

Confirmations

4,789,923

Mined by

⛏️ P2SHAGsfTT7kfefpUCYQL2XRTv84o2Y2uVxLNw

Merkle Root

60a9b4153ed143f6f570bcea7a67b7cc2102378c71d2b2b204686f694b504fc7
Transactions (2)
Coinbase96eb2c6448e1cb…cc32116ced8a47
1 in β†’ 1 out8.8100 XPM109 B
AGsfTT7k…Y2uVxLNw
2d0d0691867d02…c12e1162350f55
53 in β†’ 2 out500.0100 XPM7.74 KB
AdUbFbQ9…MXLm2P1GANo3p9rB…GMULt5kG
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.

1.515 Γ— 10⁹⁴(95-digit number)
15151368577642624993…56221542104621229721
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
1.515 Γ— 10⁹⁴(95-digit number)
15151368577642624993…56221542104621229721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.030 Γ— 10⁹⁴(95-digit number)
30302737155285249987…12443084209242459441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.060 Γ— 10⁹⁴(95-digit number)
60605474310570499974…24886168418484918881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.212 Γ— 10⁹⁡(96-digit number)
12121094862114099994…49772336836969837761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.424 Γ— 10⁹⁡(96-digit number)
24242189724228199989…99544673673939675521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.848 Γ— 10⁹⁡(96-digit number)
48484379448456399979…99089347347879351041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.696 Γ— 10⁹⁡(96-digit number)
96968758896912799959…98178694695758702081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.939 Γ— 10⁹⁢(97-digit number)
19393751779382559991…96357389391517404161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.878 Γ— 10⁹⁢(97-digit number)
38787503558765119983…92714778783034808321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.757 Γ— 10⁹⁢(97-digit number)
77575007117530239967…85429557566069616641
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:57,969,518 XPMΒ·at block #6,840,646 Β· updates every 60s
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