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Block #861,878

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/21/2014, 7:59:54 AM Β· Difficulty 10.9637 Β· 5,934,568 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a442f8d3d5b01943089b312d90af3dfed9ead74870fe2e48b2d619dbc69d818a
View on Chainz β†—

Height

#861,878

Difficulty

10.963696

Transactions

2

Size

85.52 KB

Version

2

Bits

0af6b4cb

Nonce

270,477,325

Timestamp

12/21/2014, 7:59:54 AM

Confirmations

5,934,568

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

42142c8a945ea4259b9cf40351d74f810f872052750096f4376be0246fd3723c
Transactions (2)
Coinbased97da669449f39…a676e7007df49a
1 in β†’ 1 out9.1900 XPM116 B
ANSXnLY2…Sd25TjkD
16aadf05ca064f…234a98b93c86de
590 in β†’ 1 out3697.9796 XPM85.32 KB
Ac56GA5a…kE6u4vxp
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.

7.913 Γ— 10⁹⁴(95-digit number)
79133087049971987218…36223874404239561761
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
7.913 Γ— 10⁹⁴(95-digit number)
79133087049971987218…36223874404239561761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.582 Γ— 10⁹⁡(96-digit number)
15826617409994397443…72447748808479123521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.165 Γ— 10⁹⁡(96-digit number)
31653234819988794887…44895497616958247041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.330 Γ— 10⁹⁡(96-digit number)
63306469639977589774…89790995233916494081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.266 Γ— 10⁹⁢(97-digit number)
12661293927995517954…79581990467832988161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.532 Γ— 10⁹⁢(97-digit number)
25322587855991035909…59163980935665976321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.064 Γ— 10⁹⁢(97-digit number)
50645175711982071819…18327961871331952641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.012 Γ— 10⁹⁷(98-digit number)
10129035142396414363…36655923742663905281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.025 Γ— 10⁹⁷(98-digit number)
20258070284792828727…73311847485327810561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.051 Γ— 10⁹⁷(98-digit number)
40516140569585657455…46623694970655621121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.103 Γ— 10⁹⁷(98-digit number)
81032281139171314911…93247389941311242241
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:57,615,561 XPMΒ·at block #6,796,445 Β· updates every 60s
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