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Block #155,662

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2013, 11:44:46 AM Β· Difficulty 9.8659 Β· 6,654,736 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5014f76b034c5c7e354de9934b52244330d2e4426921a0e3ea6723027acd5d4a
View on Chainz β†—

Height

#155,662

Difficulty

9.865933

Transactions

2

Size

4.81 KB

Version

2

Bits

09ddadcb

Nonce

269,473

Timestamp

9/8/2013, 11:44:46 AM

Confirmations

6,654,736

Mined by

⛏️ P2SHAZgKw9HXyHRuxwbbrK3y9zLQvifmphw4wh

Merkle Root

5600174518088d3251c6cdd3044b00a341a60724a84d7bb5e360157f96955fed
Transactions (2)
Coinbaseb53aa9695f7698…98e77e2e619bb2
1 in β†’ 1 out10.3100 XPM109 B
AZgKw9HX…fmphw4wh
2e012150f0d621…b2f14372cb39f4
41 in β†’ 1 out421.6600 XPM4.62 KB
AJs27LEf…M76myr9t
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.

9.926 Γ— 10⁹³(94-digit number)
99260135107302182667…50003432110645758401
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
9.926 Γ— 10⁹³(94-digit number)
99260135107302182667…50003432110645758401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.985 Γ— 10⁹⁴(95-digit number)
19852027021460436533…00006864221291516801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.970 Γ— 10⁹⁴(95-digit number)
39704054042920873066…00013728442583033601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.940 Γ— 10⁹⁴(95-digit number)
79408108085841746133…00027456885166067201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.588 Γ— 10⁹⁡(96-digit number)
15881621617168349226…00054913770332134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.176 Γ— 10⁹⁡(96-digit number)
31763243234336698453…00109827540664268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.352 Γ— 10⁹⁡(96-digit number)
63526486468673396906…00219655081328537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.270 Γ— 10⁹⁢(97-digit number)
12705297293734679381…00439310162657075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.541 Γ— 10⁹⁢(97-digit number)
25410594587469358762…00878620325314150401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,727,261 XPMΒ·at block #6,810,397 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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