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Block #101,597

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/6/2013, 5:20:17 PM Β· Difficulty 9.4676 Β· 6,701,636 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7eae3b8e4e31edc0cf8702ad79d7e7445307f4f669028b554bb2c7337d9c8d4d
View on Chainz β†—

Height

#101,597

Difficulty

9.467604

Transactions

1

Size

200 B

Version

2

Bits

0977b4e7

Nonce

41,516

Timestamp

8/6/2013, 5:20:17 PM

Confirmations

6,701,636

Mined by

⛏️ P2SHAZ29sR79QusQVNF36wMX1odggdnKVqwKGr

Merkle Root

dffed4ae6c4bab359bd1462867ff61a3f1d509888ec2b88b6c3628708cccdfd1
Transactions (1)
Coinbasedffed4ae6c4bab…3628708cccdfd1
1 in β†’ 1 out11.1400 XPM109 B
AZ29sR79…nKVqwKGr
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.

9.412 Γ— 10⁹⁷(98-digit number)
94129908542691412086…37735224443986916241
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
9.412 Γ— 10⁹⁷(98-digit number)
94129908542691412086…37735224443986916241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.882 Γ— 10⁹⁸(99-digit number)
18825981708538282417…75470448887973832481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.765 Γ— 10⁹⁸(99-digit number)
37651963417076564834…50940897775947664961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.530 Γ— 10⁹⁸(99-digit number)
75303926834153129669…01881795551895329921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.506 Γ— 10⁹⁹(100-digit number)
15060785366830625933…03763591103790659841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.012 Γ— 10⁹⁹(100-digit number)
30121570733661251867…07527182207581319681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.024 Γ— 10⁹⁹(100-digit number)
60243141467322503735…15054364415162639361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.204 Γ— 10¹⁰⁰(101-digit number)
12048628293464500747…30108728830325278721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.409 Γ— 10¹⁰⁰(101-digit number)
24097256586929001494…60217457660650557441
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:57,669,891 XPMΒ·at block #6,803,232 Β· updates every 60s
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