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Block #103,121

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2013, 10:56:15 AM Β· Difficulty 9.5157 Β· 6,692,234 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b854eb07b55b299d4ae2a85a040270a3a455a2b195c822705e654fe6e2ebb8b4
View on Chainz β†—

Height

#103,121

Difficulty

9.515709

Transactions

1

Size

200 B

Version

2

Bits

0984057d

Nonce

13,503

Timestamp

8/7/2013, 10:56:15 AM

Confirmations

6,692,234

Mined by

⛏️ P2SHAWuDuxGXKEXYj7RYhx64EdJKzBtLDpHWp7

Merkle Root

c79f7e61357d4af9c260664af42228b2edc16830360d582b786f04a1c723b4b1
Transactions (1)
Coinbasec79f7e61357d4a…6f04a1c723b4b1
1 in β†’ 1 out11.0300 XPM109 B
AWuDuxGX…tLDpHWp7
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.

1.460 Γ— 10⁹⁷(98-digit number)
14606269888219389349…41429385992984403999
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
1.460 Γ— 10⁹⁷(98-digit number)
14606269888219389349…41429385992984403999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.921 Γ— 10⁹⁷(98-digit number)
29212539776438778698…82858771985968807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.842 Γ— 10⁹⁷(98-digit number)
58425079552877557396…65717543971937615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁸(99-digit number)
11685015910575511479…31435087943875231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.337 Γ— 10⁹⁸(99-digit number)
23370031821151022958…62870175887750463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.674 Γ— 10⁹⁸(99-digit number)
46740063642302045917…25740351775500927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.348 Γ— 10⁹⁸(99-digit number)
93480127284604091834…51480703551001855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.869 Γ— 10⁹⁹(100-digit number)
18696025456920818366…02961407102003711999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.739 Γ— 10⁹⁹(100-digit number)
37392050913841636733…05922814204007423999
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:57,606,894 XPMΒ·at block #6,795,354 Β· updates every 60s
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