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Block #1,268,259

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/5/2015, 3:30:53 PM Β· Difficulty 10.8173 Β· 5,548,695 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
19d53dde6bcf1ba527a9a447d1a8fc0710b871c71559b5e685fd229715e3b5bd
View on Chainz β†—

Height

#1,268,259

Difficulty

10.817297

Transactions

2

Size

431 B

Version

2

Bits

0ad13a60

Nonce

1,599,871,909

Timestamp

10/5/2015, 3:30:53 PM

Confirmations

5,548,695

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

f36e32a6ba6056b7f0e3b303d20f35f5f19345dfa48725f6918f859820aa2540
Transactions (2)
Coinbasec8958f31515ed0…7f305564996f31
1 in β†’ 1 out8.5400 XPM116 B
AJCEY9yy…tg97E6zm
e2a615bab2854b…259b84ce848704
1 in β†’ 2 out1.4580 XPM225 B
AJiVRWo4…PwXGg6xLARqv8Lwm…Jt2HBwKy
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.

1.301 Γ— 10⁹⁡(96-digit number)
13016999141246883271…22300201408170259201
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
1.301 Γ— 10⁹⁡(96-digit number)
13016999141246883271…22300201408170259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.603 Γ— 10⁹⁡(96-digit number)
26033998282493766542…44600402816340518401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.206 Γ— 10⁹⁡(96-digit number)
52067996564987533084…89200805632681036801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.041 Γ— 10⁹⁢(97-digit number)
10413599312997506616…78401611265362073601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.082 Γ— 10⁹⁢(97-digit number)
20827198625995013233…56803222530724147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.165 Γ— 10⁹⁢(97-digit number)
41654397251990026467…13606445061448294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.330 Γ— 10⁹⁢(97-digit number)
83308794503980052935…27212890122896588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.666 Γ— 10⁹⁷(98-digit number)
16661758900796010587…54425780245793177601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.332 Γ— 10⁹⁷(98-digit number)
33323517801592021174…08851560491586355201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.664 Γ— 10⁹⁷(98-digit number)
66647035603184042348…17703120983172710401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,779,667 XPMΒ·at block #6,816,953 Β· updates every 60s
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