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Block #156,908

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 6:43:41 AM Β· Difficulty 9.8688 Β· 6,650,698 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ec5037012cdfb212fe7b7dd072e81930f23ecbd8142fd6e0d0d928005bc6ee85
View on Chainz β†—

Height

#156,908

Difficulty

9.868760

Transactions

2

Size

2.35 KB

Version

2

Bits

09de6715

Nonce

142,742

Timestamp

9/9/2013, 6:43:41 AM

Confirmations

6,650,698

Mined by

⛏️ P2SHAFn59p5isJugxPTD29vZX7R4uH1tLYmSWX

Merkle Root

ce09ae84bace8e6ad9151a0505668f00849941e63c6ead827a61d56a13443ebd
Transactions (2)
Coinbasee6468b1e50aeda…8aafe742bdb9aa
1 in β†’ 1 out10.2800 XPM109 B
AFn59p5i…1tLYmSWX
2a4ad3cb2eb47a…d25d879f793945
19 in β†’ 1 out195.0400 XPM2.16 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.

2.052 Γ— 10⁹⁢(97-digit number)
20527446237745533214…11710434648694401921
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
2.052 Γ— 10⁹⁢(97-digit number)
20527446237745533214…11710434648694401921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.105 Γ— 10⁹⁢(97-digit number)
41054892475491066428…23420869297388803841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.210 Γ— 10⁹⁢(97-digit number)
82109784950982132856…46841738594777607681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.642 Γ— 10⁹⁷(98-digit number)
16421956990196426571…93683477189555215361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.284 Γ— 10⁹⁷(98-digit number)
32843913980392853142…87366954379110430721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.568 Γ— 10⁹⁷(98-digit number)
65687827960785706284…74733908758220861441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.313 Γ— 10⁹⁸(99-digit number)
13137565592157141256…49467817516441722881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.627 Γ— 10⁹⁸(99-digit number)
26275131184314282513…98935635032883445761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.255 Γ— 10⁹⁸(99-digit number)
52550262368628565027…97871270065766891521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.051 Γ— 10⁹⁹(100-digit number)
10510052473725713005…95742540131533783041
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:57,704,878 XPMΒ·at block #6,807,605 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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