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Block #2,749,619

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/15/2018, 6:30:04 AM Β· Difficulty 11.6469 Β· 4,084,331 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6bf75919f42eeccf2b09b4c4c10369b2c4335e295657bedfeca8cb3ff5b07464
View on Chainz β†—

Height

#2,749,619

Difficulty

11.646947

Transactions

2

Size

1.58 KB

Version

2

Bits

0ba59e4b

Nonce

1,176,037,460

Timestamp

7/15/2018, 6:30:04 AM

Confirmations

4,084,331

Mined by

⛏️ P2SHAQ3hvGRnnAAvvMhH3Msq7LDhhsa5kZY3SG

Merkle Root

de5b6709c1126d804eba9c8513bcf6ab60eaf543a428326980db2baddddae590
Transactions (2)
Coinbasef8001a8329e912…5f27e5ef918683
1 in β†’ 1 out7.3800 XPM110 B
AQ3hvGRn…a5kZY3SG
b9da0b8fe7c8d6…76a87be59e4fec
9 in β†’ 2 out8837.8600 XPM1.38 KB
AHQy4zE5…fjwXyK3nAa8Hjvx6…CtR9Tqew
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.

2.198 Γ— 10⁹⁡(96-digit number)
21987628040910748458…86136164534648375041
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
2.198 Γ— 10⁹⁡(96-digit number)
21987628040910748458…86136164534648375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.397 Γ— 10⁹⁡(96-digit number)
43975256081821496917…72272329069296750081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.795 Γ— 10⁹⁡(96-digit number)
87950512163642993834…44544658138593500161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.759 Γ— 10⁹⁢(97-digit number)
17590102432728598766…89089316277187000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.518 Γ— 10⁹⁢(97-digit number)
35180204865457197533…78178632554374000641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.036 Γ— 10⁹⁢(97-digit number)
70360409730914395067…56357265108748001281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.407 Γ— 10⁹⁷(98-digit number)
14072081946182879013…12714530217496002561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.814 Γ— 10⁹⁷(98-digit number)
28144163892365758026…25429060434992005121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.628 Γ— 10⁹⁷(98-digit number)
56288327784731516053…50858120869984010241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.125 Γ— 10⁹⁸(99-digit number)
11257665556946303210…01716241739968020481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.251 Γ— 10⁹⁸(99-digit number)
22515331113892606421…03432483479936040961
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:57,915,829 XPMΒ·at block #6,833,949 Β· updates every 60s
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