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Block #2,836,803

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2018, 1:46:53 AM Β· Difficulty 11.7170 Β· 4,002,148 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
34b253b5a379180f042f219617dafa62b33da090c35a1d9052e42dc0c9ead165
View on Chainz β†—

Height

#2,836,803

Difficulty

11.716958

Transactions

2

Size

426 B

Version

2

Bits

0bb78a91

Nonce

151,872,628

Timestamp

9/13/2018, 1:46:53 AM

Confirmations

4,002,148

Mined by

⛏️ P2SHAQgjst1r9yACJqPcN3Zf4ZsbL3ekX2p8qR

Merkle Root

ecdb7943ca51b1aa290545104e546068a122b75dedd9ac2e945e149684068f36
Transactions (2)
Coinbasee80105eb60e8ad…a1f755a78028c3
1 in β†’ 1 out7.2800 XPM110 B
AQgjst1r…ekX2p8qR
8f66d4f55ce45b…39abaf6b264f3d
1 in β†’ 2 out30.8971 XPM225 B
AHA6SgZm…q3RZwujwAQmjqzoU…5U6sbve9
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.

2.700 Γ— 10⁹⁢(97-digit number)
27007123366900318825…91078442790067056639
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
2.700 Γ— 10⁹⁢(97-digit number)
27007123366900318825…91078442790067056639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.401 Γ— 10⁹⁢(97-digit number)
54014246733800637650…82156885580134113279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁷(98-digit number)
10802849346760127530…64313771160268226559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.160 Γ— 10⁹⁷(98-digit number)
21605698693520255060…28627542320536453119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.321 Γ— 10⁹⁷(98-digit number)
43211397387040510120…57255084641072906239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.642 Γ— 10⁹⁷(98-digit number)
86422794774081020240…14510169282145812479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.728 Γ— 10⁹⁸(99-digit number)
17284558954816204048…29020338564291624959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.456 Γ— 10⁹⁸(99-digit number)
34569117909632408096…58040677128583249919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.913 Γ— 10⁹⁸(99-digit number)
69138235819264816192…16081354257166499839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.382 Γ— 10⁹⁹(100-digit number)
13827647163852963238…32162708514332999679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.765 Γ— 10⁹⁹(100-digit number)
27655294327705926476…64325417028665999359
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:57,955,875 XPMΒ·at block #6,838,950 Β· updates every 60s
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