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Block #2,277,237

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/1/2017, 4:31:41 AM Β· Difficulty 10.9551 Β· 4,565,365 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
85a29933462f0bd0c3bfc754749db233d509c2df62435af144477807828c6bbb
View on Chainz β†—

Height

#2,277,237

Difficulty

10.955099

Transactions

2

Size

424 B

Version

2

Bits

0af48159

Nonce

621,893,009

Timestamp

9/1/2017, 4:31:41 AM

Confirmations

4,565,365

Mined by

⛏️ P2SHAY9GRNbYyMi87j7HPz3w5usCFp8q2n2ivv

Merkle Root

3595346742adbaf65c8c845f25d8d9d8bec68f3fdd980ce745a998d25f1049d5
Transactions (2)
Coinbase31470b0a408306…f685cd9871b504
1 in β†’ 1 out8.3300 XPM109 B
AY9GRNbY…8q2n2ivv
508f285c57374d…557774c41fbe8d
1 in β†’ 2 out2517.0402 XPM225 B
AQ8iuEkW…wngPGBB9AeuA49jN…Joy5i6AD
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.

1.437 Γ— 10⁹⁴(95-digit number)
14372442446072126427…48430172179425548001
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
1.437 Γ— 10⁹⁴(95-digit number)
14372442446072126427…48430172179425548001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.874 Γ— 10⁹⁴(95-digit number)
28744884892144252854…96860344358851096001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.748 Γ— 10⁹⁴(95-digit number)
57489769784288505708…93720688717702192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.149 Γ— 10⁹⁡(96-digit number)
11497953956857701141…87441377435404384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.299 Γ— 10⁹⁡(96-digit number)
22995907913715402283…74882754870808768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.599 Γ— 10⁹⁡(96-digit number)
45991815827430804566…49765509741617536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.198 Γ— 10⁹⁡(96-digit number)
91983631654861609133…99531019483235072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.839 Γ— 10⁹⁢(97-digit number)
18396726330972321826…99062038966470144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.679 Γ— 10⁹⁢(97-digit number)
36793452661944643653…98124077932940288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.358 Γ— 10⁹⁢(97-digit number)
73586905323889287306…96248155865880576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.471 Γ— 10⁹⁷(98-digit number)
14717381064777857461…92496311731761152001
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:57,985,244 XPMΒ·at block #6,842,601 Β· updates every 60s
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