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Block #749,381

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/2/2014, 4:39:57 AM Β· Difficulty 10.9765 Β· 6,094,559 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f8f5096eba648cc3474edb9c81ad89d6c53f4feaf95209b59cb037ff455ae6f
View on Chainz β†—

Height

#749,381

Difficulty

10.976485

Transactions

2

Size

546 B

Version

2

Bits

0af9faec

Nonce

1,158,371,061

Timestamp

10/2/2014, 4:39:57 AM

Confirmations

6,094,559

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cf293eeb7447712b0b455ec25fbf8f99eef458798c36cd65459fd7532c5b5404
Transactions (2)
Coinbase0e4344727880b2…2fccfaaee283c5
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
7837366b939a16…3e3c4707ed1c4f
2 in β†’ 1 out349.9900 XPM340 B
ARkumKR4…hB2QFDKB
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.

1.045 Γ— 10⁹⁡(96-digit number)
10458873137440753718…58171231065975321381
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
1.045 Γ— 10⁹⁡(96-digit number)
10458873137440753718…58171231065975321381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.091 Γ— 10⁹⁡(96-digit number)
20917746274881507437…16342462131950642761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.183 Γ— 10⁹⁡(96-digit number)
41835492549763014875…32684924263901285521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.367 Γ— 10⁹⁡(96-digit number)
83670985099526029751…65369848527802571041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.673 Γ— 10⁹⁢(97-digit number)
16734197019905205950…30739697055605142081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.346 Γ— 10⁹⁢(97-digit number)
33468394039810411900…61479394111210284161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.693 Γ— 10⁹⁢(97-digit number)
66936788079620823801…22958788222420568321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.338 Γ— 10⁹⁷(98-digit number)
13387357615924164760…45917576444841136641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.677 Γ— 10⁹⁷(98-digit number)
26774715231848329520…91835152889682273281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.354 Γ— 10⁹⁷(98-digit number)
53549430463696659041…83670305779364546561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.070 Γ— 10⁹⁸(99-digit number)
10709886092739331808…67340611558729093121
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:57,995,896 XPMΒ·at block #6,843,939 Β· updates every 60s
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