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Block #2,186,296

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/30/2017, 12:31:07 PM Β· Difficulty 10.9455 Β· 4,623,771 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a2fc7127716e4fdcb6f338b371e6415a198f7bb3cf80cd1f11711d3c875dbddf
View on Chainz β†—

Height

#2,186,296

Difficulty

10.945520

Transactions

2

Size

29.30 KB

Version

2

Bits

0af20d91

Nonce

4,445,276

Timestamp

6/30/2017, 12:31:07 PM

Confirmations

4,623,771

Mined by

⛏️ P2SHAXdpS9BX45ykMjuG4LQFE3QxEf5rdm1eV8

Merkle Root

f66dcc89e0b21db775d3f813e5c9af35ddf747a44c9b4c3de8bc32c0b337702f
Transactions (2)
Coinbase2e2da4ffaffba8…fbfd39c63c06c7
1 in β†’ 1 out8.6500 XPM110 B
AXdpS9BX…5rdm1eV8
f0d53e58efccde…d263be579f1748
201 in β†’ 1 out2.1336 XPM29.10 KB
AcT1APhs…mLCisoWP
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.

1.312 Γ— 10⁹⁴(95-digit number)
13120113015939876105…77341061930478474239
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
1.312 Γ— 10⁹⁴(95-digit number)
13120113015939876105…77341061930478474239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.624 Γ— 10⁹⁴(95-digit number)
26240226031879752211…54682123860956948479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.248 Γ— 10⁹⁴(95-digit number)
52480452063759504422…09364247721913896959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.049 Γ— 10⁹⁡(96-digit number)
10496090412751900884…18728495443827793919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.099 Γ— 10⁹⁡(96-digit number)
20992180825503801769…37456990887655587839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.198 Γ— 10⁹⁡(96-digit number)
41984361651007603538…74913981775311175679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.396 Γ— 10⁹⁡(96-digit number)
83968723302015207076…49827963550622351359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.679 Γ— 10⁹⁢(97-digit number)
16793744660403041415…99655927101244702719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.358 Γ— 10⁹⁢(97-digit number)
33587489320806082830…99311854202489405439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.717 Γ— 10⁹⁢(97-digit number)
67174978641612165660…98623708404978810879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.343 Γ— 10⁹⁷(98-digit number)
13434995728322433132…97247416809957621759
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:57,724,608 XPMΒ·at block #6,810,066 Β· updates every 60s
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