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Block #2,742,315

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/10/2018, 8:26:03 AM Β· Difficulty 11.6310 Β· 4,102,942 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2dee86240252a282a630f3bdaffbbfc8a2e70a60de67bc553acff9076a658cb6
View on Chainz β†—

Height

#2,742,315

Difficulty

11.630978

Transactions

2

Size

394 B

Version

2

Bits

0ba187c0

Nonce

175,087,177

Timestamp

7/10/2018, 8:26:03 AM

Confirmations

4,102,942

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

b4575a55eb240d1cc6794dcafcc4456bae1a4cf8e0850ce034ca5475422fa126
Transactions (2)
Coinbasec87945ac718b12…28585daf915352
1 in β†’ 1 out7.3900 XPM110 B
AZtxQr2F…7grUWrUz
606b0aa6e79965…c8f71759fa4e96
1 in β†’ 1 out3.9900 XPM193 B
AW1VQNrh…AuseDjPW
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.

6.752 Γ— 10⁹⁢(97-digit number)
67523421235928660242…45345094522974697599
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
6.752 Γ— 10⁹⁢(97-digit number)
67523421235928660242…45345094522974697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.350 Γ— 10⁹⁷(98-digit number)
13504684247185732048…90690189045949395199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.700 Γ— 10⁹⁷(98-digit number)
27009368494371464096…81380378091898790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.401 Γ— 10⁹⁷(98-digit number)
54018736988742928193…62760756183797580799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.080 Γ— 10⁹⁸(99-digit number)
10803747397748585638…25521512367595161599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.160 Γ— 10⁹⁸(99-digit number)
21607494795497171277…51043024735190323199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.321 Γ— 10⁹⁸(99-digit number)
43214989590994342555…02086049470380646399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.642 Γ— 10⁹⁸(99-digit number)
86429979181988685110…04172098940761292799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.728 Γ— 10⁹⁹(100-digit number)
17285995836397737022…08344197881522585599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.457 Γ— 10⁹⁹(100-digit number)
34571991672795474044…16688395763045171199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.914 Γ— 10⁹⁹(100-digit number)
69143983345590948088…33376791526090342399
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:58,006,489 XPMΒ·at block #6,845,256 Β· updates every 60s
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