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Block #905,240

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/22/2015, 12:52:08 PM Β· Difficulty 10.9361 Β· 5,901,043 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c73ee6d1f1df3659b2a24273e0dfa7e4245258ab3657db55ce35c8b498b9526
View on Chainz β†—

Height

#905,240

Difficulty

10.936065

Transactions

2

Size

5.51 KB

Version

2

Bits

0aefa1ee

Nonce

438,881,522

Timestamp

1/22/2015, 12:52:08 PM

Confirmations

5,901,043

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ba476eff935b41107ad13766f0722a65f5f8746149722e5bbd6b2e826a81ddf0
Transactions (2)
Coinbase7934ea39c34380…0652d54a146b00
1 in β†’ 1 out8.4600 XPM116 B
ANSXnLY2…Sd25TjkD
ccccb00da7f2e8…2af23c24c6e742
36 in β†’ 3 out8511.8711 XPM5.31 KB
ARFU6YNK…RFXZ4iUFANGTb4nb…F8oAXf6gAUSxVrre…B27XD3yv
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.

8.548 Γ— 10⁹⁴(95-digit number)
85482154927573094276…42639758373735907461
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
8.548 Γ— 10⁹⁴(95-digit number)
85482154927573094276…42639758373735907461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.709 Γ— 10⁹⁡(96-digit number)
17096430985514618855…85279516747471814921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.419 Γ— 10⁹⁡(96-digit number)
34192861971029237710…70559033494943629841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.838 Γ— 10⁹⁡(96-digit number)
68385723942058475421…41118066989887259681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.367 Γ— 10⁹⁢(97-digit number)
13677144788411695084…82236133979774519361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.735 Γ— 10⁹⁢(97-digit number)
27354289576823390168…64472267959549038721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.470 Γ— 10⁹⁢(97-digit number)
54708579153646780337…28944535919098077441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.094 Γ— 10⁹⁷(98-digit number)
10941715830729356067…57889071838196154881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.188 Γ— 10⁹⁷(98-digit number)
21883431661458712134…15778143676392309761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.376 Γ— 10⁹⁷(98-digit number)
43766863322917424269…31556287352784619521
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:57,694,350 XPMΒ·at block #6,806,282 Β· updates every 60s
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