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Block #2,877,495

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/12/2018, 2:30:11 AM Β· Difficulty 11.6488 Β· 3,964,008 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0bd79810e1f3a6efcea2379162837e64b83830443543d2622512c5f5e526eaef
View on Chainz β†—

Height

#2,877,495

Difficulty

11.648759

Transactions

1

Size

200 B

Version

2

Bits

0ba61515

Nonce

718,196,168

Timestamp

10/12/2018, 2:30:11 AM

Confirmations

3,964,008

Mined by

⛏️ P2SHANqknS8xzgrxwnbtC84eBfSWMFMBpRGy3t

Merkle Root

f678b132f98a041b39ef38ba8b074de1104555fb5349eb8346c9ac0c90ec58e7
Transactions (1)
Coinbasef678b132f98a04…c9ac0c90ec58e7
1 in β†’ 1 out7.3600 XPM110 B
ANqknS8x…MBpRGy3t
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.

3.188 Γ— 10⁹⁴(95-digit number)
31886140089163589107…55686662334053140759
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
3.188 Γ— 10⁹⁴(95-digit number)
31886140089163589107…55686662334053140759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.377 Γ— 10⁹⁴(95-digit number)
63772280178327178214…11373324668106281519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.275 Γ— 10⁹⁡(96-digit number)
12754456035665435642…22746649336212563039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.550 Γ— 10⁹⁡(96-digit number)
25508912071330871285…45493298672425126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.101 Γ— 10⁹⁡(96-digit number)
51017824142661742571…90986597344850252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.020 Γ— 10⁹⁢(97-digit number)
10203564828532348514…81973194689700504319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.040 Γ— 10⁹⁢(97-digit number)
20407129657064697028…63946389379401008639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.081 Γ— 10⁹⁢(97-digit number)
40814259314129394057…27892778758802017279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.162 Γ— 10⁹⁢(97-digit number)
81628518628258788115…55785557517604034559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.632 Γ— 10⁹⁷(98-digit number)
16325703725651757623…11571115035208069119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.265 Γ— 10⁹⁷(98-digit number)
32651407451303515246…23142230070416138239
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:57,976,402 XPMΒ·at block #6,841,502 Β· updates every 60s
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