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Block #2,124,008

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2017, 3:41:58 PM Β· Difficulty 10.9173 Β· 4,708,571 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1704d2053caa5b407dd29fda9d313e98da99fc83bdd5e8002af37afac983bedf
View on Chainz β†—

Height

#2,124,008

Difficulty

10.917285

Transactions

2

Size

425 B

Version

2

Bits

0aead334

Nonce

160,925,665

Timestamp

5/19/2017, 3:41:58 PM

Confirmations

4,708,571

Mined by

⛏️ P2SHAHRTtLwFeGtLVbmaf1aJ9n4X3EjL4jFpca

Merkle Root

f86af707f8eef6a3f24d8fff5b0c1c70c6a297f6b8867a016e16cf95490c0d12
Transactions (2)
Coinbase7e3c7595f06e0b…137b0511ac91bd
1 in β†’ 1 out8.3900 XPM109 B
AHRTtLwF…jL4jFpca
f229088414a67e…9763bfad048c95
1 in β†’ 2 out4.3202 XPM226 B
Ae9KDBqA…U5jBo9PFANfYmR5g…nB9aX4Tp
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.

4.064 Γ— 10⁹⁡(96-digit number)
40644644135185947093…18195190945528576001
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
4.064 Γ— 10⁹⁡(96-digit number)
40644644135185947093…18195190945528576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.128 Γ— 10⁹⁡(96-digit number)
81289288270371894186…36390381891057152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.625 Γ— 10⁹⁢(97-digit number)
16257857654074378837…72780763782114304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.251 Γ— 10⁹⁢(97-digit number)
32515715308148757674…45561527564228608001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.503 Γ— 10⁹⁢(97-digit number)
65031430616297515349…91123055128457216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.300 Γ— 10⁹⁷(98-digit number)
13006286123259503069…82246110256914432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.601 Γ— 10⁹⁷(98-digit number)
26012572246519006139…64492220513828864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.202 Γ— 10⁹⁷(98-digit number)
52025144493038012279…28984441027657728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.040 Γ— 10⁹⁸(99-digit number)
10405028898607602455…57968882055315456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.081 Γ— 10⁹⁸(99-digit number)
20810057797215204911…15937764110630912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.162 Γ— 10⁹⁸(99-digit number)
41620115594430409823…31875528221261824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
8.324 Γ— 10⁹⁸(99-digit number)
83240231188860819647…63751056442523648001
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:57,904,792 XPMΒ·at block #6,832,578 Β· updates every 60s
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