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Block #2,149,715

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/7/2017, 6:05:43 AM Β· Difficulty 10.8984 Β· 4,681,402 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1f249991b6550690349f7f8620106bae48e1895af4371684290bfbff9bb0758a
View on Chainz β†—

Height

#2,149,715

Difficulty

10.898388

Transactions

1

Size

208 B

Version

2

Bits

0ae5fcbd

Nonce

153,506,641

Timestamp

6/7/2017, 6:05:43 AM

Confirmations

4,681,402

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

6a98a40bcaab929ee1b1c68d28fbb61108de57585fb34f26904440631c5b187c
Transactions (1)
Coinbase6a98a40bcaab92…4440631c5b187c
1 in β†’ 1 out8.4100 XPM118 B
AM6GYpjw…aw86QDtR
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.

3.587 Γ— 10⁹⁴(95-digit number)
35873742546251770938…05378817835886015999
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
3.587 Γ— 10⁹⁴(95-digit number)
35873742546251770938…05378817835886015999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.174 Γ— 10⁹⁴(95-digit number)
71747485092503541877…10757635671772031999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.434 Γ— 10⁹⁡(96-digit number)
14349497018500708375…21515271343544063999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.869 Γ— 10⁹⁡(96-digit number)
28698994037001416751…43030542687088127999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.739 Γ— 10⁹⁡(96-digit number)
57397988074002833502…86061085374176255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.147 Γ— 10⁹⁢(97-digit number)
11479597614800566700…72122170748352511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.295 Γ— 10⁹⁢(97-digit number)
22959195229601133400…44244341496705023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.591 Γ— 10⁹⁢(97-digit number)
45918390459202266801…88488682993410047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.183 Γ— 10⁹⁢(97-digit number)
91836780918404533603…76977365986820095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.836 Γ— 10⁹⁷(98-digit number)
18367356183680906720…53954731973640191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.673 Γ— 10⁹⁷(98-digit number)
36734712367361813441…07909463947280383999
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:57,893,081 XPMΒ·at block #6,831,116 Β· updates every 60s
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