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Block #3,361,159

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/19/2019, 1:13:01 PM Β· Difficulty 10.9957 Β· 3,481,630 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d00a5420c860172a6138b1a577e3ccf3603db44bee8da22465ab764154aa1e69
View on Chainz β†—

Height

#3,361,159

Difficulty

10.995715

Transactions

1

Size

198 B

Version

2

Bits

0afee731

Nonce

2,037,011,511

Timestamp

9/19/2019, 1:13:01 PM

Confirmations

3,481,630

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

ee0025fb3250678143dbd93451d7249d3ef2138d850bc0d3e43350c967dfe514
Transactions (1)
Coinbaseee0025fb325067…3350c967dfe514
1 in β†’ 1 out8.2600 XPM109 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.

2.981 Γ— 10⁹³(94-digit number)
29815080799747301751…81818572254341472699
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
2.981 Γ— 10⁹³(94-digit number)
29815080799747301751…81818572254341472699
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.963 Γ— 10⁹³(94-digit number)
59630161599494603503…63637144508682945399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.192 Γ— 10⁹⁴(95-digit number)
11926032319898920700…27274289017365890799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.385 Γ— 10⁹⁴(95-digit number)
23852064639797841401…54548578034731781599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.770 Γ— 10⁹⁴(95-digit number)
47704129279595682803…09097156069463563199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.540 Γ— 10⁹⁴(95-digit number)
95408258559191365606…18194312138927126399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.908 Γ— 10⁹⁡(96-digit number)
19081651711838273121…36388624277854252799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.816 Γ— 10⁹⁡(96-digit number)
38163303423676546242…72777248555708505599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.632 Γ— 10⁹⁡(96-digit number)
76326606847353092485…45554497111417011199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.526 Γ— 10⁹⁢(97-digit number)
15265321369470618497…91108994222834022399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.053 Γ— 10⁹⁢(97-digit number)
30530642738941236994…82217988445668044799
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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