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Block #3,436,007

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2019, 10:18:23 PM Β· Difficulty 10.9790 Β· 3,390,954 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0bdd01d49b882b7f67ab751288a77a1a4903886a9d2df34107b88585faddbf30
View on Chainz β†—

Height

#3,436,007

Difficulty

10.979042

Transactions

1

Size

201 B

Version

2

Bits

0afaa284

Nonce

521,371,927

Timestamp

11/16/2019, 10:18:23 PM

Confirmations

3,390,954

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

47aedddf44603e1dcb528763ff6910a817e9062a92a3f482b59b692ad98c72fd
Transactions (1)
Coinbase47aedddf44603e…9b692ad98c72fd
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
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.

8.724 Γ— 10⁹⁡(96-digit number)
87245490968390415842…54227570130130155519
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.724 Γ— 10⁹⁡(96-digit number)
87245490968390415842…54227570130130155519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.744 Γ— 10⁹⁢(97-digit number)
17449098193678083168…08455140260260311039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.489 Γ— 10⁹⁢(97-digit number)
34898196387356166336…16910280520520622079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.979 Γ— 10⁹⁢(97-digit number)
69796392774712332673…33820561041041244159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.395 Γ— 10⁹⁷(98-digit number)
13959278554942466534…67641122082082488319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.791 Γ— 10⁹⁷(98-digit number)
27918557109884933069…35282244164164976639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.583 Γ— 10⁹⁷(98-digit number)
55837114219769866139…70564488328329953279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.116 Γ— 10⁹⁸(99-digit number)
11167422843953973227…41128976656659906559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.233 Γ— 10⁹⁸(99-digit number)
22334845687907946455…82257953313319813119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.466 Γ— 10⁹⁸(99-digit number)
44669691375815892911…64515906626639626239
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,859,864 XPMΒ·at block #6,826,960 Β· updates every 60s
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