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Block #2,699,099

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 6/10/2018, 4:27:58 AM Β· Difficulty 11.6455 Β· 4,132,780 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
19a3ec89ef5b8474b24a7fb5b95bc47d7dc60bc0f61aac838429a8b6bc89c28c
View on Chainz β†—

Height

#2,699,099

Difficulty

11.645469

Transactions

2

Size

1020 B

Version

2

Bits

0ba53d71

Nonce

599,904,042

Timestamp

6/10/2018, 4:27:58 AM

Confirmations

4,132,780

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

106a25fff843e021e71de39136caa411222a15311d5c8105dcb3011c4ca5ea40
Transactions (2)
Coinbase1547d3f278bb59…4608212caca9e8
1 in β†’ 1 out7.3700 XPM110 B
AZtxQr2F…7grUWrUz
f318b65eefd37b…80ac2b362ad3d5
5 in β†’ 2 out5796.4640 XPM820 B
AbpzauYH…L1MJHE4CATthx4jz…VhbvxDTr
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.

2.618 Γ— 10⁹⁡(96-digit number)
26187126948310957964…53285422827996118399
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
2.618 Γ— 10⁹⁡(96-digit number)
26187126948310957964…53285422827996118399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.237 Γ— 10⁹⁡(96-digit number)
52374253896621915928…06570845655992236799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.047 Γ— 10⁹⁢(97-digit number)
10474850779324383185…13141691311984473599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.094 Γ— 10⁹⁢(97-digit number)
20949701558648766371…26283382623968947199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.189 Γ— 10⁹⁢(97-digit number)
41899403117297532742…52566765247937894399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.379 Γ— 10⁹⁢(97-digit number)
83798806234595065485…05133530495875788799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.675 Γ— 10⁹⁷(98-digit number)
16759761246919013097…10267060991751577599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.351 Γ— 10⁹⁷(98-digit number)
33519522493838026194…20534121983503155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.703 Γ— 10⁹⁷(98-digit number)
67039044987676052388…41068243967006310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.340 Γ— 10⁹⁸(99-digit number)
13407808997535210477…82136487934012620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.681 Γ— 10⁹⁸(99-digit number)
26815617995070420955…64272975868025241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
5.363 Γ— 10⁹⁸(99-digit number)
53631235990140841911…28545951736050483199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,899,154 XPMΒ·at block #6,831,878 Β· updates every 60s
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