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Block #1,120,676

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2015, 7:53:47 AM Β· Difficulty 10.9360 Β· 5,686,447 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ffc97182599f1b7a62c353f077487eecaf1b38f568874d548c66b033ac936be0
View on Chainz β†—

Height

#1,120,676

Difficulty

10.936016

Transactions

2

Size

5.33 KB

Version

2

Bits

0aef9ebb

Nonce

836,719,632

Timestamp

6/21/2015, 7:53:47 AM

Confirmations

5,686,447

Mined by

⛏️ P2SHAVH5PUcszhVp44nGeqzU8Nb7fcFEtf5GKT

Merkle Root

64692c0c10b4dae5e620cd130181f19f0c5ba6eadd56e1c5a4f80a153148a6e7
Transactions (2)
Coinbase55d52b85f14315…6f0ea937d4cf62
1 in β†’ 1 out8.4100 XPM110 B
AVH5PUcs…FEtf5GKT
f83240344eee0d…36b7cfad7024c4
35 in β†’ 2 out180.0000 XPM5.13 KB
AYneSKCP…vQrb9efdAGky5ni4…jnaoQ88P
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.

3.262 Γ— 10⁹⁴(95-digit number)
32620262020610454951…93200075609526906539
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
3.262 Γ— 10⁹⁴(95-digit number)
32620262020610454951…93200075609526906539
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.262 Γ— 10⁹⁴(95-digit number)
32620262020610454951…93200075609526906541
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
6.524 Γ— 10⁹⁴(95-digit number)
65240524041220909903…86400151219053813079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.524 Γ— 10⁹⁴(95-digit number)
65240524041220909903…86400151219053813081
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
1.304 Γ— 10⁹⁡(96-digit number)
13048104808244181980…72800302438107626159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.304 Γ— 10⁹⁡(96-digit number)
13048104808244181980…72800302438107626161
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
2.609 Γ— 10⁹⁡(96-digit number)
26096209616488363961…45600604876215252319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.609 Γ— 10⁹⁡(96-digit number)
26096209616488363961…45600604876215252321
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
5.219 Γ— 10⁹⁡(96-digit number)
52192419232976727922…91201209752430504639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.219 Γ— 10⁹⁡(96-digit number)
52192419232976727922…91201209752430504641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,701,087 XPMΒ·at block #6,807,122 Β· updates every 60s
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