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Block #1,729,653

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/22/2016, 9:57:38 PM Β· Difficulty 10.7111 Β· 5,077,104 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
217e9260a181ac639ea8d3457a2f61a5e3bc672cb7bf76b0639365f209e6974e
View on Chainz β†—

Height

#1,729,653

Difficulty

10.711106

Transactions

2

Size

868 B

Version

2

Bits

0ab60b04

Nonce

770,002,996

Timestamp

8/22/2016, 9:57:38 PM

Confirmations

5,077,104

Mined by

⛏️ P2SHAauU3pSj9sTLFwmq1SaeLKCz5vCt8C7U7c

Merkle Root

33a99d41134abf4b9aa8878c97ec1c4a6f31a69568afb6576a93ad982a4b9c8f
Transactions (2)
Coinbase71d2b2cbef8148…d0f9220687392d
1 in β†’ 1 out8.7100 XPM109 B
AauU3pSj…Ct8C7U7c
4f82ee982d07bb…2f68078a1c77ec
4 in β†’ 2 out10400.8957 XPM670 B
AMP7EGhn…hgQDQGEcAPiEeYs4…nP6ueLor
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.

1.606 Γ— 10⁹³(94-digit number)
16067190754975743995…74608015370352553601
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
1.606 Γ— 10⁹³(94-digit number)
16067190754975743995…74608015370352553601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.213 Γ— 10⁹³(94-digit number)
32134381509951487991…49216030740705107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.426 Γ— 10⁹³(94-digit number)
64268763019902975982…98432061481410214401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.285 Γ— 10⁹⁴(95-digit number)
12853752603980595196…96864122962820428801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.570 Γ— 10⁹⁴(95-digit number)
25707505207961190392…93728245925640857601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.141 Γ— 10⁹⁴(95-digit number)
51415010415922380785…87456491851281715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.028 Γ— 10⁹⁡(96-digit number)
10283002083184476157…74912983702563430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.056 Γ— 10⁹⁡(96-digit number)
20566004166368952314…49825967405126860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.113 Γ— 10⁹⁡(96-digit number)
41132008332737904628…99651934810253721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.226 Γ— 10⁹⁡(96-digit number)
82264016665475809257…99303869620507443201
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:57,698,156 XPMΒ·at block #6,806,756 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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