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Block #3,436,699

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/17/2019, 9:54:24 AM Β· Difficulty 10.9790 Β· 3,403,176 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
144ef93ee31ac18f878deea3e4a8d014537c43fac238ac780b055dc663b818cc
View on Chainz β†—

Height

#3,436,699

Difficulty

10.979030

Transactions

2

Size

2.83 KB

Version

2

Bits

0afaa1bc

Nonce

1,694,889,983

Timestamp

11/17/2019, 9:54:24 AM

Confirmations

3,403,176

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

9805a29be3ab8a512c7c7a7271e08bd625f5ca7f864bfac71c4ef3da196f36df
Transactions (2)
Coinbase62f31419d980a7…e0372c7e1b816a
1 in β†’ 1 out8.3100 XPM110 B
ASiq2qtK…VMhmk7yL
6dd3e2740ecc81…1bb61eb2631274
18 in β†’ 1 out180.9205 XPM2.63 KB
AXoSyMCe…Z8KXiWkn
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.

2.707 Γ— 10⁹⁡(96-digit number)
27073909781853430877…49904982965624106681
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
2.707 Γ— 10⁹⁡(96-digit number)
27073909781853430877…49904982965624106681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.414 Γ— 10⁹⁡(96-digit number)
54147819563706861755…99809965931248213361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.082 Γ— 10⁹⁢(97-digit number)
10829563912741372351…99619931862496426721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.165 Γ— 10⁹⁢(97-digit number)
21659127825482744702…99239863724992853441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.331 Γ— 10⁹⁢(97-digit number)
43318255650965489404…98479727449985706881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.663 Γ— 10⁹⁢(97-digit number)
86636511301930978808…96959454899971413761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.732 Γ— 10⁹⁷(98-digit number)
17327302260386195761…93918909799942827521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.465 Γ— 10⁹⁷(98-digit number)
34654604520772391523…87837819599885655041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.930 Γ— 10⁹⁷(98-digit number)
69309209041544783047…75675639199771310081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.386 Γ— 10⁹⁸(99-digit number)
13861841808308956609…51351278399542620161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,963,301 XPMΒ·at block #6,839,874 Β· updates every 60s
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