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Block #3,439,366

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2019, 7:22:17 AM Β· Difficulty 10.9789 Β· 3,400,209 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aee00d821ef0d9f015c382263dcad18f323e99f863c71ed03282658c6e8bc114
View on Chainz β†—

Height

#3,439,366

Difficulty

10.978856

Transactions

2

Size

1.68 KB

Version

2

Bits

0afa9649

Nonce

870,168,639

Timestamp

11/19/2019, 7:22:17 AM

Confirmations

3,400,209

Mined by

⛏️ P2SHAa32y8PQmrraS9AMzCsmSNxawTe3Enbehj

Merkle Root

9b1df8257adac8e8a55e44be92cb6348312e5940c0b68d8e3c64763e15935b19
Transactions (2)
Coinbase9cc017f2f91415…4b19b8e5c1b814
1 in β†’ 1 out8.3000 XPM109 B
Aa32y8PQ…e3Enbehj
158545b71b87ab…66e745e640370a
10 in β†’ 1 out100.5181 XPM1.48 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.

2.851 Γ— 10⁹⁢(97-digit number)
28519975347143252561…60754943859658588161
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
2.851 Γ— 10⁹⁢(97-digit number)
28519975347143252561…60754943859658588161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.703 Γ— 10⁹⁢(97-digit number)
57039950694286505122…21509887719317176321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.140 Γ— 10⁹⁷(98-digit number)
11407990138857301024…43019775438634352641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.281 Γ— 10⁹⁷(98-digit number)
22815980277714602048…86039550877268705281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.563 Γ— 10⁹⁷(98-digit number)
45631960555429204097…72079101754537410561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.126 Γ— 10⁹⁷(98-digit number)
91263921110858408195…44158203509074821121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.825 Γ— 10⁹⁸(99-digit number)
18252784222171681639…88316407018149642241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.650 Γ— 10⁹⁸(99-digit number)
36505568444343363278…76632814036299284481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.301 Γ— 10⁹⁸(99-digit number)
73011136888686726556…53265628072598568961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.460 Γ— 10⁹⁹(100-digit number)
14602227377737345311…06531256145197137921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.920 Γ— 10⁹⁹(100-digit number)
29204454755474690622…13062512290394275841
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
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