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Block #857,258

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2014, 5:09:52 PM Β· Difficulty 10.9676 Β· 5,982,832 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d528b775e74d29456efb806224df58aaa929a8c9d659f58d24d0dd1a8f456c85
View on Chainz β†—

Height

#857,258

Difficulty

10.967572

Transactions

1

Size

206 B

Version

2

Bits

0af7b2cb

Nonce

285,093,459

Timestamp

12/17/2014, 5:09:52 PM

Confirmations

5,982,832

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

102447965cd65ddaabc8b02a4693e7f45862efd0b8004684b50921d7acde07be
Transactions (1)
Coinbase102447965cd65d…0921d7acde07be
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.700 Γ— 10⁹⁡(96-digit number)
17009282021819016828…49120432138353202401
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
1.700 Γ— 10⁹⁡(96-digit number)
17009282021819016828…49120432138353202401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.401 Γ— 10⁹⁡(96-digit number)
34018564043638033657…98240864276706404801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.803 Γ— 10⁹⁡(96-digit number)
68037128087276067315…96481728553412809601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.360 Γ— 10⁹⁢(97-digit number)
13607425617455213463…92963457106825619201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.721 Γ— 10⁹⁢(97-digit number)
27214851234910426926…85926914213651238401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.442 Γ— 10⁹⁢(97-digit number)
54429702469820853852…71853828427302476801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.088 Γ— 10⁹⁷(98-digit number)
10885940493964170770…43707656854604953601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.177 Γ— 10⁹⁷(98-digit number)
21771880987928341540…87415313709209907201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.354 Γ— 10⁹⁷(98-digit number)
43543761975856683081…74830627418419814401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.708 Γ— 10⁹⁷(98-digit number)
87087523951713366163…49661254836839628801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.741 Γ— 10⁹⁸(99-digit number)
17417504790342673232…99322509673679257601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,965,030 XPMΒ·at block #6,840,089 Β· updates every 60s
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