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Block #70,564

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 2:15:39 PM Β· Difficulty 8.9923 Β· 6,735,526 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de6b2897b0b4aec4a4ae6ac217cd7b3667e8721b7f2a074016c403b1efaba5e9
View on Chainz β†—

Height

#70,564

Difficulty

8.992289

Transactions

1

Size

198 B

Version

2

Bits

08fe06a4

Nonce

31

Timestamp

7/20/2013, 2:15:39 PM

Confirmations

6,735,526

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

30ea057008ac21df8ba3127d3d485bdba67e54a7cdfd9e0b9c7eda78fb85457e
Transactions (1)
Coinbase30ea057008ac21…7eda78fb85457e
1 in β†’ 1 out12.3500 XPM110 B
AXSFye4r…ADf1YWCU
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.

3.309 Γ— 10⁸⁹(90-digit number)
33096887486588421542…59801342330135355459
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.309 Γ— 10⁸⁹(90-digit number)
33096887486588421542…59801342330135355459
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.619 Γ— 10⁸⁹(90-digit number)
66193774973176843085…19602684660270710919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.323 Γ— 10⁹⁰(91-digit number)
13238754994635368617…39205369320541421839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.647 Γ— 10⁹⁰(91-digit number)
26477509989270737234…78410738641082843679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.295 Γ— 10⁹⁰(91-digit number)
52955019978541474468…56821477282165687359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.059 Γ— 10⁹¹(92-digit number)
10591003995708294893…13642954564331374719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.118 Γ— 10⁹¹(92-digit number)
21182007991416589787…27285909128662749439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.236 Γ— 10⁹¹(92-digit number)
42364015982833179574…54571818257325498879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.472 Γ— 10⁹¹(92-digit number)
84728031965666359149…09143636514650997759
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,692,792 XPMΒ·at block #6,806,089 Β· updates every 60s
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