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Block #53,437

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/16/2013, 3:22:50 PM Β· Difficulty 8.9235 Β· 6,754,672 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a3c6ee8766264f5d8b89d79c5c1b3d51e2bcfa7d3b804faf818c1ece2a382b1c
View on Chainz β†—

Height

#53,437

Difficulty

8.923477

Transactions

1

Size

199 B

Version

2

Bits

08ec6900

Nonce

82

Timestamp

7/16/2013, 3:22:50 PM

Confirmations

6,754,672

Mined by

⛏️ P2SHAGY4TBx7s42EHEAbrwoVx7JoxEYfD8h7Va

Merkle Root

d7fb4270226cc4ce55959110a82afd19b02faae9472385ca0776e3d65324e28e
Transactions (1)
Coinbased7fb4270226cc4…76e3d65324e28e
1 in β†’ 1 out12.5400 XPM110 B
AGY4TBx7…YfD8h7Va
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.

3.341 Γ— 10⁹²(93-digit number)
33416368871493614619…01040341099206220719
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
3.341 Γ— 10⁹²(93-digit number)
33416368871493614619…01040341099206220719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.683 Γ— 10⁹²(93-digit number)
66832737742987229239…02080682198412441439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.336 Γ— 10⁹³(94-digit number)
13366547548597445847…04161364396824882879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.673 Γ— 10⁹³(94-digit number)
26733095097194891695…08322728793649765759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.346 Γ— 10⁹³(94-digit number)
53466190194389783391…16645457587299531519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁴(95-digit number)
10693238038877956678…33290915174599063039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.138 Γ— 10⁹⁴(95-digit number)
21386476077755913356…66581830349198126079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.277 Γ— 10⁹⁴(95-digit number)
42772952155511826713…33163660698396252159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.554 Γ— 10⁹⁴(95-digit number)
85545904311023653426…66327321396792504319
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:57,708,919 XPMΒ·at block #6,808,108 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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