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Block #111,900

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/11/2013, 5:08:27 PM Β· Difficulty 9.7140 Β· 6,684,385 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c1b1f1c434620cc4c9b044ae85085f59fcb045d94cd8398b49bc32ed71fcb118
View on Chainz β†—

Height

#111,900

Difficulty

9.713953

Transactions

1

Size

200 B

Version

2

Bits

09b6c5a5

Nonce

36,841

Timestamp

8/11/2013, 5:08:27 PM

Confirmations

6,684,385

Mined by

⛏️ P2SHASXW8s4r1QTq8Djg6zDrh4WCnULM8vqY9U

Merkle Root

bb323b2638118858192a12953ced0826737744e9917ccae70716ee0e43fbaaa3
Transactions (1)
Coinbasebb323b26381188…16ee0e43fbaaa3
1 in β†’ 1 out10.5800 XPM109 B
ASXW8s4r…LM8vqY9U
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.

1.819 Γ— 10⁹⁸(99-digit number)
18191601788597418697…38080956065739377579
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
1.819 Γ— 10⁹⁸(99-digit number)
18191601788597418697…38080956065739377579
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.819 Γ— 10⁹⁸(99-digit number)
18191601788597418697…38080956065739377581
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
3.638 Γ— 10⁹⁸(99-digit number)
36383203577194837394…76161912131478755159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.638 Γ— 10⁹⁸(99-digit number)
36383203577194837394…76161912131478755161
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
7.276 Γ— 10⁹⁸(99-digit number)
72766407154389674789…52323824262957510319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.276 Γ— 10⁹⁸(99-digit number)
72766407154389674789…52323824262957510321
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
1.455 Γ— 10⁹⁹(100-digit number)
14553281430877934957…04647648525915020639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.455 Γ— 10⁹⁹(100-digit number)
14553281430877934957…04647648525915020641
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
2.910 Γ— 10⁹⁹(100-digit number)
29106562861755869915…09295297051830041279
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:57,614,283 XPMΒ·at block #6,796,284 Β· updates every 60s
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