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Block #1,214,774

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/30/2015, 7:38:31 PM Β· Difficulty 10.7319 Β· 5,602,704 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
80d916aaa8dc80909df57c517bb9afc8c7a6f8b9d77467a506825b197cba861b
View on Chainz β†—

Height

#1,214,774

Difficulty

10.731933

Transactions

2

Size

876 B

Version

2

Bits

0abb5ff7

Nonce

55,261,433

Timestamp

8/30/2015, 7:38:31 PM

Confirmations

5,602,704

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

07db9295d77aced50103d96fbfd59304d26b21743e46f13f4ac0c751ad056774
Transactions (2)
Coinbase434fe97e400a90…4c98283e20f816
1 in β†’ 1 out8.6800 XPM116 B
AJCEY9yy…tg97E6zm
e4e6ba07d1201a…d16ebfe280de35
4 in β†’ 2 out43.6835 XPM669 B
ASxsnr1w…5JKcMfzFAHhem1Zi…ooRrsR7Y
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.

2.834 Γ— 10⁹⁢(97-digit number)
28345275208347018532…14570512716652159681
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
2.834 Γ— 10⁹⁢(97-digit number)
28345275208347018532…14570512716652159681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.669 Γ— 10⁹⁢(97-digit number)
56690550416694037064…29141025433304319361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.133 Γ— 10⁹⁷(98-digit number)
11338110083338807412…58282050866608638721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.267 Γ— 10⁹⁷(98-digit number)
22676220166677614825…16564101733217277441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.535 Γ— 10⁹⁷(98-digit number)
45352440333355229651…33128203466434554881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.070 Γ— 10⁹⁷(98-digit number)
90704880666710459303…66256406932869109761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.814 Γ— 10⁹⁸(99-digit number)
18140976133342091860…32512813865738219521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.628 Γ— 10⁹⁸(99-digit number)
36281952266684183721…65025627731476439041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.256 Γ— 10⁹⁸(99-digit number)
72563904533368367442…30051255462952878081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.451 Γ— 10⁹⁹(100-digit number)
14512780906673673488…60102510925905756161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.902 Γ— 10⁹⁹(100-digit number)
29025561813347346977…20205021851811512321
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:57,783,877 XPMΒ·at block #6,817,477 Β· updates every 60s
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