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Block #1,102,946

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2015, 5:39:37 PM Β· Difficulty 10.7523 Β· 5,722,520 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1bd38679684777191f0a02aa4be01587cdbe5e779ed5545a9e8a7244cd107d31
View on Chainz β†—

Height

#1,102,946

Difficulty

10.752339

Transactions

2

Size

538 B

Version

2

Bits

0ac0994f

Nonce

1,765,767,795

Timestamp

6/13/2015, 5:39:37 PM

Confirmations

5,722,520

Mined by

⛏️ P2SHALHafvpufMuxPARCAKMMXVshhv7P7T93nB

Merkle Root

288ebdc6b8cb036ac39c64d5e8d48868779dd0105255c33a4386db5cda9b6e4d
Transactions (2)
Coinbase963b7265ff79bb…2206856a5daf9d
1 in β†’ 1 out8.6500 XPM109 B
ALHafvpu…7P7T93nB
eb892d800f5327…f298fc8d9cbfe3
2 in β†’ 1 out0.9900 XPM339 B
Acb1xA8z…9ActivN8
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.

5.419 Γ— 10⁹⁴(95-digit number)
54194968999785595210…58733167386845843839
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
5.419 Γ— 10⁹⁴(95-digit number)
54194968999785595210…58733167386845843839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁡(96-digit number)
10838993799957119042…17466334773691687679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.167 Γ— 10⁹⁡(96-digit number)
21677987599914238084…34932669547383375359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.335 Γ— 10⁹⁡(96-digit number)
43355975199828476168…69865339094766750719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.671 Γ— 10⁹⁡(96-digit number)
86711950399656952337…39730678189533501439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.734 Γ— 10⁹⁢(97-digit number)
17342390079931390467…79461356379067002879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.468 Γ— 10⁹⁢(97-digit number)
34684780159862780934…58922712758134005759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.936 Γ— 10⁹⁢(97-digit number)
69369560319725561869…17845425516268011519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁷(98-digit number)
13873912063945112373…35690851032536023039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.774 Γ— 10⁹⁷(98-digit number)
27747824127890224747…71381702065072046079
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:57,847,831 XPMΒ·at block #6,825,465 Β· updates every 60s
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