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Block #2,126,472

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/21/2017, 6:47:45 AM Β· Difficulty 10.9193 Β· 4,705,230 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3bd4b55d0a0514368c8b2b36b4a392cdcf5a5bba882e9127cad626648b22f464
View on Chainz β†—

Height

#2,126,472

Difficulty

10.919286

Transactions

2

Size

2.84 KB

Version

2

Bits

0aeb5651

Nonce

199,340,978

Timestamp

5/21/2017, 6:47:45 AM

Confirmations

4,705,230

Mined by

⛏️ P2SHAaMp2bdeUtpAgsZ41uyaoahYBKLbyU9KjN

Merkle Root

dc570a1f4520946aecb8151c5548aef8cd573dc7d1a63ed907fe91c1a360a41d
Transactions (2)
Coinbase6c74b3eea14adc…7a55cdc8b76cc2
1 in β†’ 1 out8.4000 XPM110 B
AaMp2bde…LbyU9KjN
480bec846badfd…ca58faf3c69b56
18 in β†’ 1 out1534.4153 XPM2.64 KB
AUoBdDi8…m7dZunoP
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.

4.203 Γ— 10⁹⁢(97-digit number)
42035400027663865148…46984995246851107841
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
4.203 Γ— 10⁹⁢(97-digit number)
42035400027663865148…46984995246851107841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.407 Γ— 10⁹⁢(97-digit number)
84070800055327730296…93969990493702215681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.681 Γ— 10⁹⁷(98-digit number)
16814160011065546059…87939980987404431361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.362 Γ— 10⁹⁷(98-digit number)
33628320022131092118…75879961974808862721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.725 Γ— 10⁹⁷(98-digit number)
67256640044262184236…51759923949617725441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.345 Γ— 10⁹⁸(99-digit number)
13451328008852436847…03519847899235450881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.690 Γ— 10⁹⁸(99-digit number)
26902656017704873694…07039695798470901761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.380 Γ— 10⁹⁸(99-digit number)
53805312035409747389…14079391596941803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.076 Γ— 10⁹⁹(100-digit number)
10761062407081949477…28158783193883607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.152 Γ— 10⁹⁹(100-digit number)
21522124814163898955…56317566387767214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.304 Γ— 10⁹⁹(100-digit number)
43044249628327797911…12635132775534428161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
8.608 Γ— 10⁹⁹(100-digit number)
86088499256655595823…25270265551068856321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,897,725 XPMΒ·at block #6,831,701 Β· updates every 60s
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