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Block #70,977

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 4:27:49 PM Β· Difficulty 8.9927 Β· 6,738,876 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
26fa8b23b3938a32e264dd26495a7ca9fa3f9ab26d830851f7cf65346bb7d1b2
View on Chainz β†—

Height

#70,977

Difficulty

8.992718

Transactions

1

Size

199 B

Version

2

Bits

08fe22c3

Nonce

174

Timestamp

7/20/2013, 4:27:49 PM

Confirmations

6,738,876

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

8863ccb469e14082ea8f7ad3dbdd3c0761ea5bd531d0cd315bb13daaa6bc13ff
Transactions (1)
Coinbase8863ccb469e140…b13daaa6bc13ff
1 in β†’ 1 out12.3500 XPM110 B
AZDgU5ry…dmcwdqVC
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.

2.321 Γ— 10⁹³(94-digit number)
23218266393130775153…76785858551403644391
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
2.321 Γ— 10⁹³(94-digit number)
23218266393130775153…76785858551403644391
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.643 Γ— 10⁹³(94-digit number)
46436532786261550306…53571717102807288781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.287 Γ— 10⁹³(94-digit number)
92873065572523100612…07143434205614577561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.857 Γ— 10⁹⁴(95-digit number)
18574613114504620122…14286868411229155121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.714 Γ— 10⁹⁴(95-digit number)
37149226229009240244…28573736822458310241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.429 Γ— 10⁹⁴(95-digit number)
74298452458018480489…57147473644916620481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.485 Γ— 10⁹⁡(96-digit number)
14859690491603696097…14294947289833240961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.971 Γ— 10⁹⁡(96-digit number)
29719380983207392195…28589894579666481921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.943 Γ— 10⁹⁡(96-digit number)
59438761966414784391…57179789159332963841
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:57,722,911 XPMΒ·at block #6,809,852 Β· updates every 60s
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