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Block #3,437,948

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/18/2019, 8:15:36 AM Β· Difficulty 10.9787 Β· 3,403,559 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3eecb25cef131a22e181d454b971dde45529e40e3300d19c72a93e036cd848e4
View on Chainz β†—

Height

#3,437,948

Difficulty

10.978680

Transactions

2

Size

1.54 KB

Version

2

Bits

0afa8abe

Nonce

359,132,395

Timestamp

11/18/2019, 8:15:36 AM

Confirmations

3,403,559

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

b655d70a4ee2dbebcafde2961f35642e6a4befd36781950ebbfde87955af0add
Transactions (2)
Coinbase186e944fc3af3f…d378ef4de76656
1 in β†’ 1 out8.3000 XPM110 B
ASiq2qtK…VMhmk7yL
125a62e9100f87…f3a4b5f983407b
9 in β†’ 1 out90.4067 XPM1.34 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.

1.588 Γ— 10⁹⁡(96-digit number)
15889720394841888780…10643613971313456611
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
1.588 Γ— 10⁹⁡(96-digit number)
15889720394841888780…10643613971313456611
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.177 Γ— 10⁹⁡(96-digit number)
31779440789683777560…21287227942626913221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.355 Γ— 10⁹⁡(96-digit number)
63558881579367555120…42574455885253826441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.271 Γ— 10⁹⁢(97-digit number)
12711776315873511024…85148911770507652881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.542 Γ— 10⁹⁢(97-digit number)
25423552631747022048…70297823541015305761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.084 Γ— 10⁹⁢(97-digit number)
50847105263494044096…40595647082030611521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.016 Γ— 10⁹⁷(98-digit number)
10169421052698808819…81191294164061223041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.033 Γ— 10⁹⁷(98-digit number)
20338842105397617638…62382588328122446081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.067 Γ— 10⁹⁷(98-digit number)
40677684210795235277…24765176656244892161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.135 Γ— 10⁹⁷(98-digit number)
81355368421590470554…49530353312489784321
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:57,976,435 XPMΒ·at block #6,841,506 Β· updates every 60s
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