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Block #223,224

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/22/2013, 8:10:22 PM Β· Difficulty 9.9387 Β· 6,593,122 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
eb01a853b6e9fa4b59d8e586a23832b7bcf3d9713d102a3bc60ea074b2aa9a67
View on Chainz β†—

Height

#223,224

Difficulty

9.938681

Transactions

2

Size

688 B

Version

2

Bits

09f04d66

Nonce

109,371

Timestamp

10/22/2013, 8:10:22 PM

Confirmations

6,593,122

Mined by

⛏️ P2SHAJNnxqXcDFPTjxCa13QejzdRfFHj9ayqaW

Merkle Root

ac02441cd04a17abb826bb71c45e38b191a4b1ab79fcdee96ae0df314a22314f
Transactions (2)
Coinbase1863022cc1d003…1e4cd67ca6c126
1 in β†’ 1 out10.1200 XPM109 B
AJNnxqXc…Hj9ayqaW
c69a88b5a45d86…bbd78ecbf79ae5
3 in β†’ 1 out8.4953 XPM489 B
ANJiFfFz…q4wZ7a81
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.

2.645 Γ— 10⁹⁴(95-digit number)
26452647503230225115…09111135468028059519
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
2.645 Γ— 10⁹⁴(95-digit number)
26452647503230225115…09111135468028059519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.645 Γ— 10⁹⁴(95-digit number)
26452647503230225115…09111135468028059521
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
5.290 Γ— 10⁹⁴(95-digit number)
52905295006460450230…18222270936056119039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.290 Γ— 10⁹⁴(95-digit number)
52905295006460450230…18222270936056119041
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
1.058 Γ— 10⁹⁡(96-digit number)
10581059001292090046…36444541872112238079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.058 Γ— 10⁹⁡(96-digit number)
10581059001292090046…36444541872112238081
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
2.116 Γ— 10⁹⁡(96-digit number)
21162118002584180092…72889083744224476159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.116 Γ— 10⁹⁡(96-digit number)
21162118002584180092…72889083744224476161
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
4.232 Γ— 10⁹⁡(96-digit number)
42324236005168360184…45778167488448952319
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:57,774,892 XPMΒ·at block #6,816,345 Β· updates every 60s
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