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Block #1,172,426

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2015, 6:47:02 AM Β· Difficulty 10.9373 Β· 5,632,707 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ebf548aa8c91d92ee41f5efe193e7f4f3cb3a1834a1c514fdfbaceadbb7eee97
View on Chainz β†—

Height

#1,172,426

Difficulty

10.937343

Transactions

2

Size

2.58 KB

Version

2

Bits

0aeff5bc

Nonce

538,293,762

Timestamp

7/27/2015, 6:47:02 AM

Confirmations

5,632,707

Mined by

⛏️ P2SHAQAddT8g3xQ5guH84eC2776yhuURghANGV

Merkle Root

2e6365b64a55f693ec41138f53034321bba7cde848a4874e2775d7b4f92d97f1
Transactions (2)
Coinbasea255c6599bfeb8…bab8ea2c687b04
1 in β†’ 1 out8.3800 XPM110 B
AQAddT8g…URghANGV
faf5b3fb3724c2…85294faff8847b
16 in β†’ 2 out524.5329 XPM2.38 KB
AJVeRHXf…C2yREH1fAGD7MwF3…9429mPPd
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.

1.624 Γ— 10⁹⁢(97-digit number)
16247776995407423789…00191504684637913599
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
1.624 Γ— 10⁹⁢(97-digit number)
16247776995407423789…00191504684637913599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.624 Γ— 10⁹⁢(97-digit number)
16247776995407423789…00191504684637913601
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
3.249 Γ— 10⁹⁢(97-digit number)
32495553990814847578…00383009369275827199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.249 Γ— 10⁹⁢(97-digit number)
32495553990814847578…00383009369275827201
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
6.499 Γ— 10⁹⁢(97-digit number)
64991107981629695156…00766018738551654399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.499 Γ— 10⁹⁢(97-digit number)
64991107981629695156…00766018738551654401
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
1.299 Γ— 10⁹⁷(98-digit number)
12998221596325939031…01532037477103308799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.299 Γ— 10⁹⁷(98-digit number)
12998221596325939031…01532037477103308801
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
2.599 Γ— 10⁹⁷(98-digit number)
25996443192651878062…03064074954206617599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.599 Γ— 10⁹⁷(98-digit number)
25996443192651878062…03064074954206617601
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:57,685,128 XPMΒ·at block #6,805,132 Β· updates every 60s
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