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Block #919,504

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/2/2015, 5:53:37 AM Β· Difficulty 10.9202 Β· 5,887,362 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb4d30fe47e9680e98ca8db3cfdaf0950fcb186b436345120c7033a7f188857e
View on Chainz β†—

Height

#919,504

Difficulty

10.920159

Transactions

2

Size

832 B

Version

2

Bits

0aeb8f8e

Nonce

458,424

Timestamp

2/2/2015, 5:53:37 AM

Confirmations

5,887,362

Mined by

⛏️ P2SHAPR6RvNMCwwS8xFM3QxxS2EdskMmAPSKJu

Merkle Root

235ef58c42430956b2af0467363dc74a218c6cfbe5fe36f1e5899163a45877cc
Transactions (2)
Coinbase4968bad694f382…c8cc10916a5865
1 in β†’ 1 out8.3800 XPM109 B
APR6RvNM…MmAPSKJu
8376cc2207f9e6…55c7f7f49c1a14
4 in β†’ 1 out24.9543 XPM633 B
AWF4rtPp…LnbQHVaN
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.

2.612 Γ— 10⁹⁡(96-digit number)
26127459725242364316…87860125655750677761
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
2.612 Γ— 10⁹⁡(96-digit number)
26127459725242364316…87860125655750677761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.225 Γ— 10⁹⁡(96-digit number)
52254919450484728633…75720251311501355521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.045 Γ— 10⁹⁢(97-digit number)
10450983890096945726…51440502623002711041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.090 Γ— 10⁹⁢(97-digit number)
20901967780193891453…02881005246005422081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.180 Γ— 10⁹⁢(97-digit number)
41803935560387782906…05762010492010844161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.360 Γ— 10⁹⁢(97-digit number)
83607871120775565812…11524020984021688321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.672 Γ— 10⁹⁷(98-digit number)
16721574224155113162…23048041968043376641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.344 Γ— 10⁹⁷(98-digit number)
33443148448310226325…46096083936086753281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.688 Γ— 10⁹⁷(98-digit number)
66886296896620452650…92192167872173506561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.337 Γ— 10⁹⁸(99-digit number)
13377259379324090530…84384335744347013121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.675 Γ— 10⁹⁸(99-digit number)
26754518758648181060…68768671488694026241
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:57,699,035 XPMΒ·at block #6,806,865 Β· updates every 60s
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