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Block #156,257

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2013, 8:26:40 PM Β· Difficulty 9.8678 Β· 6,640,587 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8f5c49b1604ecd9c61f6f9b0308fefe0521206171daa4781cb4f466660ab4944
View on Chainz β†—

Height

#156,257

Difficulty

9.867842

Transactions

2

Size

3.57 KB

Version

2

Bits

09de2ae0

Nonce

77,892

Timestamp

9/8/2013, 8:26:40 PM

Confirmations

6,640,587

Mined by

⛏️ P2SHATPMUVRYe3iTuqVwgmV82HfaW2YtxTHDNH

Merkle Root

8d969091f58394688ccf62ff570bc55f7e6d670e0e6d44353fb49a55daff16f4
Transactions (2)
Coinbasebe88f3d19014c8…0a8b63b8887af1
1 in β†’ 1 out10.2900 XPM109 B
ATPMUVRY…YtxTHDNH
dbc68a9fa5f64d…08d9d1c58be42c
30 in β†’ 1 out308.0100 XPM3.38 KB
AJs27LEf…M76myr9t
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.

3.023 Γ— 10⁹⁴(95-digit number)
30237476663990980202…62668277972778156189
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
3.023 Γ— 10⁹⁴(95-digit number)
30237476663990980202…62668277972778156189
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.047 Γ— 10⁹⁴(95-digit number)
60474953327981960404…25336555945556312379
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.209 Γ— 10⁹⁡(96-digit number)
12094990665596392080…50673111891112624759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.418 Γ— 10⁹⁡(96-digit number)
24189981331192784161…01346223782225249519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.837 Γ— 10⁹⁡(96-digit number)
48379962662385568323…02692447564450499039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.675 Γ— 10⁹⁡(96-digit number)
96759925324771136647…05384895128900998079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.935 Γ— 10⁹⁢(97-digit number)
19351985064954227329…10769790257801996159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.870 Γ— 10⁹⁢(97-digit number)
38703970129908454658…21539580515603992319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.740 Γ— 10⁹⁢(97-digit number)
77407940259816909317…43079161031207984639
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:57,618,765 XPMΒ·at block #6,796,843 Β· updates every 60s
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