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Block #227,034

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/25/2013, 3:13:59 PM Β· Difficulty 9.9362 Β· 6,588,986 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e89bdce74ce9877276ff23e576c319f75ef7f9f3706f291ac4d2a2d13b813ff8
View on Chainz β†—

Height

#227,034

Difficulty

9.936169

Transactions

2

Size

425 B

Version

2

Bits

09efa8c4

Nonce

9,834

Timestamp

10/25/2013, 3:13:59 PM

Confirmations

6,588,986

Mined by

⛏️ P2SHAb2FHWa1U4MVVGZdifgkeT4raqdMhsxpD2

Merkle Root

a007d7b8a520a4ef6520a88f268b609b2203b12bc47878ab5070d993734c438f
Transactions (2)
Coinbase6d2fb5187a4a4e…8677077ad4efce
1 in β†’ 1 out10.1200 XPM109 B
Ab2FHWa1…dMhsxpD2
3b43d4d9e26f20…49340407e62e12
1 in β†’ 2 out10.1000 XPM226 B
APzut6KR…As7hNgMYAXLhERZ8…oaTo1cPN
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.

4.808 Γ— 10⁹³(94-digit number)
48083175451674308585…33430147224089455999
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
4.808 Γ— 10⁹³(94-digit number)
48083175451674308585…33430147224089455999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.808 Γ— 10⁹³(94-digit number)
48083175451674308585…33430147224089456001
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
9.616 Γ— 10⁹³(94-digit number)
96166350903348617171…66860294448178911999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.616 Γ— 10⁹³(94-digit number)
96166350903348617171…66860294448178912001
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
1.923 Γ— 10⁹⁴(95-digit number)
19233270180669723434…33720588896357823999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.923 Γ— 10⁹⁴(95-digit number)
19233270180669723434…33720588896357824001
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
3.846 Γ— 10⁹⁴(95-digit number)
38466540361339446868…67441177792715647999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.846 Γ— 10⁹⁴(95-digit number)
38466540361339446868…67441177792715648001
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
7.693 Γ— 10⁹⁴(95-digit number)
76933080722678893737…34882355585431295999
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:57,772,272 XPMΒ·at block #6,816,019 Β· updates every 60s
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