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Block #71,469

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 6:49:51 PM Β· Difficulty 8.9932 Β· 6,738,288 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fdd12c9b2988eba6b3b5d2d7fe8451d5c4c0d9648dd7ef7c6e998d45f589c0e2
View on Chainz β†—

Height

#71,469

Difficulty

8.993221

Transactions

1

Size

204 B

Version

2

Bits

08fe43b5

Nonce

1,027

Timestamp

7/20/2013, 6:49:51 PM

Confirmations

6,738,288

Mined by

⛏️ P2SHAKZxB9sLnFagacwoGg9Nd9LCvLZhxs5zB5

Merkle Root

dba8ef13961dc515f049bb62302481e14155d118df91d29b87d303a0aade9207
Transactions (1)
Coinbasedba8ef13961dc5…d303a0aade9207
1 in β†’ 1 out12.3500 XPM110 B
AKZxB9sL…Zhxs5zB5
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.

2.429 Γ— 10¹⁰⁡(106-digit number)
24297998473510086408…53323081863321344031
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
2.429 Γ— 10¹⁰⁡(106-digit number)
24297998473510086408…53323081863321344031
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.859 Γ— 10¹⁰⁡(106-digit number)
48595996947020172817…06646163726642688061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.719 Γ— 10¹⁰⁡(106-digit number)
97191993894040345634…13292327453285376121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.943 Γ— 10¹⁰⁢(107-digit number)
19438398778808069126…26584654906570752241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.887 Γ— 10¹⁰⁢(107-digit number)
38876797557616138253…53169309813141504481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.775 Γ— 10¹⁰⁢(107-digit number)
77753595115232276507…06338619626283008961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.555 Γ— 10¹⁰⁷(108-digit number)
15550719023046455301…12677239252566017921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.110 Γ— 10¹⁰⁷(108-digit number)
31101438046092910603…25354478505132035841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.220 Γ— 10¹⁰⁷(108-digit number)
62202876092185821206…50708957010264071681
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:57,722,142 XPMΒ·at block #6,809,756 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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