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Block #902,634

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/20/2015, 12:40:49 PM Β· Difficulty 10.9395 Β· 5,896,804 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7cc75e4313daac0ecb13d3f72dc3345f411d070271c1fe932545be993109cc02
View on Chainz β†—

Height

#902,634

Difficulty

10.939525

Transactions

2

Size

4.03 KB

Version

2

Bits

0af084ba

Nonce

933,041,915

Timestamp

1/20/2015, 12:40:49 PM

Confirmations

5,896,804

Mined by

⛏️ P2SHAH6f1FnmvjUejoaKuhwbhL7mefqiNnMoA5

Merkle Root

807c8fd30e50a21f597780d290ba15da0e00c7208e1faee5dd9055960e51d13c
Transactions (2)
Coinbase21f5f6e2582874…8c5fb5c91464b5
1 in β†’ 1 out8.3800 XPM110 B
AH6f1Fnm…qiNnMoA5
1708846ec68f10…ac00e05f5c16aa
26 in β†’ 2 out4989.9100 XPM3.83 KB
AKzN1zCS…3cWf3HivAQ5KT526…tGengjpE
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.

2.906 Γ— 10⁹⁡(96-digit number)
29069688006678736349…70216783733802108159
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
2.906 Γ— 10⁹⁡(96-digit number)
29069688006678736349…70216783733802108159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.813 Γ— 10⁹⁡(96-digit number)
58139376013357472699…40433567467604216319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.162 Γ— 10⁹⁢(97-digit number)
11627875202671494539…80867134935208432639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.325 Γ— 10⁹⁢(97-digit number)
23255750405342989079…61734269870416865279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.651 Γ— 10⁹⁢(97-digit number)
46511500810685978159…23468539740833730559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.302 Γ— 10⁹⁢(97-digit number)
93023001621371956318…46937079481667461119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.860 Γ— 10⁹⁷(98-digit number)
18604600324274391263…93874158963334922239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.720 Γ— 10⁹⁷(98-digit number)
37209200648548782527…87748317926669844479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.441 Γ— 10⁹⁷(98-digit number)
74418401297097565054…75496635853339688959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.488 Γ— 10⁹⁸(99-digit number)
14883680259419513010…50993271706679377919
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:57,639,555 XPMΒ·at block #6,799,437 Β· updates every 60s
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