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Block #856,457

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2014, 2:29:30 AM Β· Difficulty 10.9681 Β· 5,959,491 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db8d6baad6ec13ee98f048a101d3a00fac509c59119465481a5fd912f91fb9dd
View on Chainz β†—

Height

#856,457

Difficulty

10.968057

Transactions

2

Size

728 B

Version

2

Bits

0af7d293

Nonce

394,832,339

Timestamp

12/17/2014, 2:29:30 AM

Confirmations

5,959,491

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cbbe7c28c45361371476280eb1e5cbb4eb4507b07f922216fdd085268409b59f
Transactions (2)
Coinbasedc48bed6474f74…52cad583a02c9c
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
70ae0799b63299…d641eb135cdba9
3 in β†’ 2 out5.0124 XPM522 B
AMPHJzn7…eDrmyVs9AKfsNVkC…aztyQ6gq
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.

1.049 Γ— 10⁹⁡(96-digit number)
10492678309102811084…98940043642346057761
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
1.049 Γ— 10⁹⁡(96-digit number)
10492678309102811084…98940043642346057761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.098 Γ— 10⁹⁡(96-digit number)
20985356618205622168…97880087284692115521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.197 Γ— 10⁹⁡(96-digit number)
41970713236411244336…95760174569384231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.394 Γ— 10⁹⁡(96-digit number)
83941426472822488673…91520349138768462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.678 Γ— 10⁹⁢(97-digit number)
16788285294564497734…83040698277536924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.357 Γ— 10⁹⁢(97-digit number)
33576570589128995469…66081396555073848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.715 Γ— 10⁹⁢(97-digit number)
67153141178257990938…32162793110147696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.343 Γ— 10⁹⁷(98-digit number)
13430628235651598187…64325586220295393281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.686 Γ— 10⁹⁷(98-digit number)
26861256471303196375…28651172440590786561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.372 Γ— 10⁹⁷(98-digit number)
53722512942606392750…57302344881181573121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.074 Γ— 10⁹⁸(99-digit number)
10744502588521278550…14604689762363146241
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:57,771,698 XPMΒ·at block #6,815,947 Β· updates every 60s
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