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Block #259,460

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/13/2013, 3:39:59 PM Β· Difficulty 9.9773 Β· 6,553,409 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a155c3da50186dce30071ed31a9890a7219b16e66db1a7d6456c85b41961c53b
View on Chainz β†—

Height

#259,460

Difficulty

9.977277

Transactions

2

Size

869 B

Version

2

Bits

09fa2ecb

Nonce

228,468

Timestamp

11/13/2013, 3:39:59 PM

Confirmations

6,553,409

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

118690dde3fb0e3d339372131f16783e79d5e3895460ab4f6d59b27ef09b4fbc
Transactions (2)
Coinbaseb544c9bdbfacb6…e041d18acce24f
1 in β†’ 1 out10.0400 XPM110 B
AeKNrjNj…1NEq95Ta
e3d3191be00d00…6a28293968e547
4 in β†’ 2 out102.8268 XPM670 B
AZdmkNt9…Dk8ffFeUATqfn844…Cnc9i4kM
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.

6.846 Γ— 10⁹¹(92-digit number)
68466914014805591162…59644659676435377119
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
6.846 Γ— 10⁹¹(92-digit number)
68466914014805591162…59644659676435377119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.369 Γ— 10⁹²(93-digit number)
13693382802961118232…19289319352870754239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.738 Γ— 10⁹²(93-digit number)
27386765605922236465…38578638705741508479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.477 Γ— 10⁹²(93-digit number)
54773531211844472930…77157277411483016959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.095 Γ— 10⁹³(94-digit number)
10954706242368894586…54314554822966033919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.190 Γ— 10⁹³(94-digit number)
21909412484737789172…08629109645932067839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.381 Γ— 10⁹³(94-digit number)
43818824969475578344…17258219291864135679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.763 Γ— 10⁹³(94-digit number)
87637649938951156688…34516438583728271359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.752 Γ— 10⁹⁴(95-digit number)
17527529987790231337…69032877167456542719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.505 Γ— 10⁹⁴(95-digit number)
35055059975580462675…38065754334913085439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,746,982 XPMΒ·at block #6,812,868 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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