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Block #2,001,213

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/27/2017, 6:22:32 AM Β· Difficulty 10.7407 Β· 4,841,738 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
237b1f06a440e2f57bd3feabc502fa18776f18abf60a87156b5b4b03fe39efaf
View on Chainz β†—

Height

#2,001,213

Difficulty

10.740671

Transactions

2

Size

9.78 KB

Version

2

Bits

0abd9c9b

Nonce

81,607,120

Timestamp

2/27/2017, 6:22:32 AM

Confirmations

4,841,738

Mined by

⛏️ P2SHAMASvK16bn33K7rAMbYZWw4UxkPf4cu6us

Merkle Root

6064f1711c6ec5fabcec8bf63dcc5538afa0881032e0a352a55bbb116c6a1b52
Transactions (2)
Coinbase7728482b146874…b9af8c52143cc8
1 in β†’ 1 out8.7700 XPM109 B
AMASvK16…Pf4cu6us
8c53a2a10f8a89…7a602d5affb576
66 in β†’ 1 out4999.9900 XPM9.58 KB
AXPJBFmA…c1YGiGCK
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.

8.344 Γ— 10⁹⁴(95-digit number)
83447485833902943197…88688894634933768881
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
8.344 Γ— 10⁹⁴(95-digit number)
83447485833902943197…88688894634933768881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.668 Γ— 10⁹⁡(96-digit number)
16689497166780588639…77377789269867537761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.337 Γ— 10⁹⁡(96-digit number)
33378994333561177278…54755578539735075521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.675 Γ— 10⁹⁡(96-digit number)
66757988667122354557…09511157079470151041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.335 Γ— 10⁹⁢(97-digit number)
13351597733424470911…19022314158940302081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.670 Γ— 10⁹⁢(97-digit number)
26703195466848941823…38044628317880604161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.340 Γ— 10⁹⁢(97-digit number)
53406390933697883646…76089256635761208321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.068 Γ— 10⁹⁷(98-digit number)
10681278186739576729…52178513271522416641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.136 Γ— 10⁹⁷(98-digit number)
21362556373479153458…04357026543044833281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.272 Γ— 10⁹⁷(98-digit number)
42725112746958306917…08714053086089666561
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:57,987,960 XPMΒ·at block #6,842,950 Β· updates every 60s
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