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Block #118,584

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2013, 9:02:38 PM Β· Difficulty 9.7510 Β· 6,708,132 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
82885d02d7e8cc6834610e70569a0b243f7ff656c924122c485a454efa6ab869
View on Chainz β†—

Height

#118,584

Difficulty

9.750982

Transactions

1

Size

200 B

Version

2

Bits

09c0405d

Nonce

5,330

Timestamp

8/15/2013, 9:02:38 PM

Confirmations

6,708,132

Mined by

⛏️ P2SHAGELmJR6aPRjt3Z8ALYc9YsGpGUuQ4Rhjr

Merkle Root

23270ef524244edbf4664135e92005d4ada480c816403e4e29206c53cfeedd3a
Transactions (1)
Coinbase23270ef524244e…206c53cfeedd3a
1 in β†’ 1 out10.5000 XPM109 B
AGELmJR6…UuQ4Rhjr
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.

1.817 Γ— 10⁹⁸(99-digit number)
18175263761339114281…31010328450532348399
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.817 Γ— 10⁹⁸(99-digit number)
18175263761339114281…31010328450532348399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.817 Γ— 10⁹⁸(99-digit number)
18175263761339114281…31010328450532348401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.635 Γ— 10⁹⁸(99-digit number)
36350527522678228563…62020656901064696799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.635 Γ— 10⁹⁸(99-digit number)
36350527522678228563…62020656901064696801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
7.270 Γ— 10⁹⁸(99-digit number)
72701055045356457126…24041313802129393599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.270 Γ— 10⁹⁸(99-digit number)
72701055045356457126…24041313802129393601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.454 Γ— 10⁹⁹(100-digit number)
14540211009071291425…48082627604258787199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.454 Γ— 10⁹⁹(100-digit number)
14540211009071291425…48082627604258787201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.908 Γ— 10⁹⁹(100-digit number)
29080422018142582850…96165255208517574399
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,857,881 XPMΒ·at block #6,826,715 Β· updates every 60s
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