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Block #1,681,450

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2016, 8:49:42 AM Β· Difficulty 10.7154 Β· 5,158,599 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a1c4a6a93bff2fb985f0b1363651ecc513a9016904732532e72fb0886361d33a
View on Chainz β†—

Height

#1,681,450

Difficulty

10.715369

Transactions

1

Size

199 B

Version

2

Bits

0ab7226e

Nonce

579,956,203

Timestamp

7/20/2016, 8:49:42 AM

Confirmations

5,158,599

Mined by

⛏️ P2SHASEcQmufUFeRXg9CGg9j4SVyEH6pM47xgD

Merkle Root

c16083109410ca162df960a6faa3a730b074e4e7014c4b162a1cf93b9efd3197
Transactions (1)
Coinbasec16083109410ca…1cf93b9efd3197
1 in β†’ 1 out8.7000 XPM109 B
ASEcQmuf…6pM47xgD
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.

4.888 Γ— 10⁹⁴(95-digit number)
48887095696199079984…03093502315524788321
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
4.888 Γ— 10⁹⁴(95-digit number)
48887095696199079984…03093502315524788321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.777 Γ— 10⁹⁴(95-digit number)
97774191392398159968…06187004631049576641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.955 Γ— 10⁹⁡(96-digit number)
19554838278479631993…12374009262099153281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.910 Γ— 10⁹⁡(96-digit number)
39109676556959263987…24748018524198306561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.821 Γ— 10⁹⁡(96-digit number)
78219353113918527974…49496037048396613121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.564 Γ— 10⁹⁢(97-digit number)
15643870622783705594…98992074096793226241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.128 Γ— 10⁹⁢(97-digit number)
31287741245567411189…97984148193586452481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.257 Γ— 10⁹⁢(97-digit number)
62575482491134822379…95968296387172904961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.251 Γ— 10⁹⁷(98-digit number)
12515096498226964475…91936592774345809921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.503 Γ— 10⁹⁷(98-digit number)
25030192996453928951…83873185548691619841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.006 Γ— 10⁹⁷(98-digit number)
50060385992907857903…67746371097383239681
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,964,700 XPMΒ·at block #6,840,048 Β· updates every 60s
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