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Block #145,882

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2013, 4:13:34 AM Β· Difficulty 9.8457 Β· 6,659,281 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7952390d922f4ca7e97d6f4e024f81e76c62097f69203492a88f468f652c4208
View on Chainz β†—

Height

#145,882

Difficulty

9.845741

Transactions

1

Size

198 B

Version

2

Bits

09d88278

Nonce

48,873

Timestamp

9/2/2013, 4:13:34 AM

Confirmations

6,659,281

Mined by

⛏️ P2SHAex8Nfcz7W3Vs2WQ3vpccQavANd1CPBmRv

Merkle Root

a28358f175f2aedeb6a0f3206bc3a9279ea9c243d434fe947beaea32be9d53ae
Transactions (1)
Coinbasea28358f175f2ae…eaea32be9d53ae
1 in β†’ 1 out10.3000 XPM109 B
Aex8Nfcz…d1CPBmRv
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.

6.929 Γ— 10⁹¹(92-digit number)
69297637073394272622…55057318951810713599
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
6.929 Γ— 10⁹¹(92-digit number)
69297637073394272622…55057318951810713599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.929 Γ— 10⁹¹(92-digit number)
69297637073394272622…55057318951810713601
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
1.385 Γ— 10⁹²(93-digit number)
13859527414678854524…10114637903621427199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.385 Γ— 10⁹²(93-digit number)
13859527414678854524…10114637903621427201
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
2.771 Γ— 10⁹²(93-digit number)
27719054829357709049…20229275807242854399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.771 Γ— 10⁹²(93-digit number)
27719054829357709049…20229275807242854401
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
5.543 Γ— 10⁹²(93-digit number)
55438109658715418098…40458551614485708799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.543 Γ— 10⁹²(93-digit number)
55438109658715418098…40458551614485708801
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
1.108 Γ— 10⁹³(94-digit number)
11087621931743083619…80917103228971417599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.108 Γ— 10⁹³(94-digit number)
11087621931743083619…80917103228971417601
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:57,685,371 XPMΒ·at block #6,805,162 Β· updates every 60s
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